1. Imaginary Numbers and Powers

Chapter 5

Complex Numbers and Quadratic Equations

Imaginary Numbers and Powers

It is a solution to the quadratic equation or expression, x²+1 = 0, such as;

x² = 0 – 1

x² = -1

x = √-1

x = i

Therefore, an imaginary number is the part of complex number which we can write like a real number multiplied by the imaginary unit i, where i² = -1. The imaginary number, when multiplied by itself, gives a negative value.

Value of Powers of i

We know, i² = -1, let us calculate the value of ‘i’ raised to the power other imaginary numbers.

i⁴ⁿ = 1
i⁴ⁿ⁺¹ = i
i⁴ⁿ⁺²= -1
i⁴ⁿ⁺³=-i