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Imaginary Numbers Chart

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An Imaginary Number is represented as x i, where 'x' is any real number and 'i' represents the constant whose Square is always -1. This constant 'i' may not be used in normal number system because of its imaginary nature. This Complex Number 'i' is purely algebraic or we can say it a number because it obey all the rules used in the mathematics. There is an imaginary Numbers chart which is discussed below:

Power of i: When we put power 0, 1, 2... on 'i' then we will get some results which are shown in this chart:

i0

1

i1

i

i2

-1

i3

-1*i = -i

i4

-i2 = -(-1) = 1

So on

So on

Even power of 'i' will always be 1 or -1 while odd powers will be in i or -i. On basis of this chart we can easily calculate imaginary numbers or complex numbers.

Property of 'i': This property defines the complex unit of 'i', that is i2 = -1. Let us see the example for this, 6i * 4i = 24 (-1) = -24, here the factor i2 changes the sign which shows negative and positive form of product or we can say the result of equation.

Negative radical: When radical is negative then it is in form of negative roots. As, √-x where x > 0. There is an example of negative radical: $\sqrt{-5}$ = $\sqrt{(-1 * 5)}$ = I $\sqrt{5}$.

Real and imaginary numbers of an equation are calculated by arranging it in form of real to real and imaginary to imaginary by complex conjugates. The product of a Complex Conjugate pair is always equals to sum of square of component. As, (x + yi) (x - yi) = x2 – y2i2 = x2 + y2.