Definition of complex number

In the previous post we have discussed about 11th Grade Math and In today's session we are going to discuss about  Definition of complex number.

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Here we are going to discuss an important concept that is complex number. Complex number can be defined as any number that can be written in the form of p + iq, here value of ‘p’ and ‘q’ stands for real number and ‘i’ stands for imaginary unit. Here value of ‘i’ is given as √ -1. In above given form ‘p’ is denoted as real part and ‘q’ is denoted as imaginary part of complex number. Complex number p + iq can also be described using the point (p, q). If its real part is given as zero then it is called as pure imaginary and if its imaginary part is zero then it is known as real number. Now we will discuss some rules of complex number.

 i = √ -1, the value of 'i' is represented as √ -1. Here if we use iota symbol in the equations then we can write the square root of negative numbers. For example: (√ x (√ y)), we can also write this given value as √ xy.

Let’s discuss some rules that are used for solve imaginary numbers. As we discussed above value of 'i' is given as √ -1, on squaring the iota we get:

= i² = √ -1 * √ -1, we get the value of i² = -1.

In case of i³ it can also write this equation in squaring form:

= i³ = i² * i; (we know that value of i² is -1).

= -1 * i = -i.

In case of i⁴, first write it in the squaring form,

= i⁴ = i² * i², put the value of i² we get:

= -1 * -1 = 1. This is all about complex number definition.

There are different types of Multiplication Properties which are identity, commutative and so on.

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11th Grade Math

Mathematics is an interesting subject, which needs innovation and practice to prove yourself. When we look at the contents taught to students till class 10, we observe that they are quite different from what child studies in grade 11. Now when we talk about topics of grade 10th, it includes the basic concepts of mathematics which includes arithmetic, geometry at basic stage, trigonometric basics too.

But moving ahead, we observe that 11th Grade Math includes the topics which are quite new for the students and are of different interest. When we learn about the integration and differentiation in beginning it looks as it we are learning some research topics. The high level mathematics helps the child to relate some of the topics of mathematics with physics. Even learning Physics becomes easy for the students of mathematics in grade 11, as many of the proofs and solving equations are based on the concepts which the child is learning in math class. Besides this we have the topic of mathematical induction, permutation and combination along with the higher level of probability, which helps the child to develop the logical skills and the reasoning concepts.

Learning mathematics in grade 11 has its own thrill, but the child need to be in the regular practice of the subject. We often observe that the science student who has opted for the mathematics in grade 11 is busy in solving the mathematical problems in about 45 – 60 % of his academics studies, and the left over subject is distributed evenly among all other subjects. Mathematics needs involvement and interest of the child to perform well in the subject.

Ordinary Differential Equations is one of the topic taught in class 11. Icse Syllabus For Class 8 is also available online and papers of different subjects can be downloaded. 

 

What is graphing exponential functions

As we all are very well aware about the concept of exponent that describe a value to the power of any number through which any number can multiplied by itself. In the same aspect exponential function can also be describe as a function which can be represented as the power of x of exponential function. This can be represented as a^x. In the section, the discussion held on the topic of graphing exponential functions. To understand the methodology of plotting a exponential function on to a graph we first need to understand why we use exponential function. The basic reason behind using a exponential function is that it is capable of modeling or representing the rate of change between the independent and dependent variable.
The exponential function is a kind of function which can be represented in the form of f (x) = a^x. In this exponential function ‘a’ is a variable which include any positive value but greater than 1. The concept of graphing an exponential function can be categorized into two categories on the basis of their shapes. When the value of variable ‘a’ of exponential function is positive but less than one then it generate a curve from top left side to right down side. On other hand when value of variable ‘a’ of exponential function is greater than one then it generate a curve of graph left down side to right top side. This function have their application in various field of real world like estimating population growth, compound interest, bacterial calculation and radioactive growth. Some time the concept of exponential function also be describe as xy^a where x is a positive value and y is also a positive value but not equal to 1.
In chemistry the concept of Properties of Acids can be describe as characteristics which is able to define the feature of acids. Indian certificate of secondary education having the syllabus of all subjects for any particular class, which is popularly known as icse syllabus 2013.

solve using matrices

In the previous post we have discussed about 11th Grade Math and In today's session we are going to discuss about solve using matrices. Matrices are defined as the set of objects or set of numbers or may be a set of characters in the form of a particular format of rows and columns. These rows and columns are defined for all matrices and a matrix is also known as two dimensional arrays. Various operations can be performed over matrices that are mathematical operations such as addition, subtraction, multiplication and inverse of a matrix can also be determined. Matrices are defined in the order “m x n” where m is the number of rows and n is the number of columns. An equation can be represented in the form of matrix, as left hand side of equals to symbol is represented in the matrix form to the left side only and similarly the right side is represented to the right side in the matrix form. Let us consider an example with the equations x + y = 5 and 3x – y = -1. These equations can be represented in the form of matrix and we will solve using matrices. Representing these equations in the form of matrix we get coefficients of x and y in one matrix and x and y in other matrix. And the constants will be represented to the right hand side in the form of matrix.

Potential energy is defined as the energy which is in the form of stored energy. Potential energy formula is given as potential energy is equals to the product of mass of object to the acceleration of gravity to the height of object. In a mathematical form it is represented as P.E= m x g x h where m is the mass of object, g is the acceleration due to gravity and h is the height of object. Icse board is similar to cbse board which runs all over India. It appears to give more practical knowledge and icse 2013 board papers can be easily discovered on net. It provides help to the students by giving an idea of questions.

11th Grade Math

In the previous post we have discussed about Standard Deviation Calculator and In today's session we are going to discuss about 11th Grade Math. The grade 11th is one of the turning points of our life that decide our professional future in a particular field. When students came in 11th standard then they need to choose particular subject like science, commerce or arts stream. In today’s life science - math is one of the popular streams which are chosen by the most of students. At the time when students came into 11th grade then they noticed that course of math in 11th grade in harder or not easy to tackle in comparison of previous year.

The interest towards the math of students gets higher when they select math stream in grade 11th. Here in this section discussion held on the topic of 11th Grade Math that helps the students when they are discussing about which stream they need to select or syllabus of math in grade 11th. The 11th Grade Math’s we generally deals with advance concept of algebra which includes some topic that are real numbers and their algebraic expressions. It also include problems that are related with 1st degree of inequalities and polynomial equations. In the calculative part of mathematics, math includes other important topic like slope of a line and their rate of change, calculative logarithm functions and matrix analysis and their equations, last but not least the concept of rational root theorem.

In the syllabus of math of 11th grade students can also understand the concept of pre calculus that deals with sequences and series, trigonometry functions and their inverse, concept of conic section, graphs and their sinusoidal functions and so on.

Some portion of 11th grade math’s include the study of statistics to handle the real world problem very easily.

Protons and Neutrons are the part of any molecules that can be consider as a nucleons which are attracted with each other by nuclei force. In school examination, for student preparation various websites pro vide 10th maths question paper to perform better in exam.  

Standard Deviation Calculator

In the previous post we have discussed about sample standard deviation calculator and In today's session we are going to discuss about Standard Deviation Calculator. Hi friends, in this blog we will discuss the definition and calculation of Standard Deviation Calculator. In mathematics, Standard Deviation can be defined as the variation exists from the given mean value or in other word expected value  or average value. Generally it is known by symbol sigma as (σ). Now we will understand the concept Standard Deviation Calculator. It is a online tool or machine which is used to find the value of standard deviation. Using this online machine we can get the vlaue of standard deviation within a second. In other word this online machine will gives us the value of standard deviation of given set of data in one click. To find the value of deviation with the help of calculator we have to understand some steps so that we can easily the answer. (know more about Standard Deviation Calculator, here)
Steps to follow to find the value of standard deviation are mention below:

Step 1: Using this online machine we can easily find the vlaue of standard deviation. so we use the formula as ∑ = √[(1 / N) Σi (xi - μ) 2].

Step 2: Here the value of ‘σ’ shows standard deviation, vlaue of ‘N’ shows the number of data Points and value of ‘Xi’ shows the Random Variable in which the value ‘i’ lies between 1 to N.

Step 3: In above formula ‘μ’ shows the mean value of the given data set. At last we have to calculate the exact value of σ. This above formula is predefined in this online machine. We have to put the data values in the text box and press the solve button to get the answer. It is very easy to use.

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sample standard deviation calculator

In the previous post we have discussed about How To Find The Range Of A Function and In today's session we are going to discuss about sample standard deviation calculator. In mathematics, sample standard deviation calculator is a online machine that is basically used to solve the standard deviation of the given data values form its mean. Those students are not know the concept of standard deviation can also use it very comfortably. This machine make the calculation so easy. In other word we can easily solve any standard problem using this calculator. Let’s understand some steps to solve standard deviation problem. (know more about standard deviation , here)

Step 1: First enter the data values in the text box.

Step 2: Then press the solve button to get the result.

In standard deviation calculator the formula defined to find standard deviation is give as:

σ= √ [(1 /N) ∑i (xi – μ)²

Step 3: ‘μ’ symbol shows mean values of data set. At last we have to write the final answer for standard deviation.

Let’s understand it with the help of small example:

Find the standard deviation for the given data values 10, 20, 30, 40.

Solution: To solve it we need to follow the above steps so that we can easily solve the standard deviation.
Step 1 : Formula to find standard deviation is given as σ = √[(1 / N) Σi (xi - μ) ²], here value of N = 4, so we find mean of given data values.

Mean = μ = 10 + 20 + 30 + 40;

μ = 100 / 4, μ = 25.
Step 2: Then find the value of (xi - μ)², xi = the random variable, i.e. 10, 20, 30, 40;

(10 - 25)² = 225,

(20 - 25)² = 25,

(30 - 25)² = 25,

(40 - 25)² = 225,

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                 = 500,

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Σ ( xi - μ )² = 500,

Step 3 : Then the variance is given as: Variance = Σ ( xi - μ )² / N,

Variance = 500 / 4, Variance = 125;
Standard deviation = σ = √[(1 / N) Σi (xi - μ)²]; put given values in formula to get answer. σ = √ [(1 / 4) 125],

At last we get the value of standard deviation is 11.180.

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