Complex Number Formula

About Complex Number Formula

A complex number is one that satisfies the equation i2 = 1 and can be represented in the form a + bi, where a and b are real numbers and i is the imaginary unit. The real part of the complex number is a, while the imaginary part is b in this formula

By employing the horizontal axis for the real part and the vertical axis for the imaginary part, complex numbers extend the concept of the one-dimensional number line to the two-dimensional complex plane.

Here are some Complex Number formulas

1. Equality of Complex Numbers Formula
   1. a + bi = c + di ⇔ a = c and b = d
2. Addition of Complex Numbers
   1. (a + bi) + (c + di) = (a - c) + (b - d)i
3. Subtraction of Complex Numbers
   1. (a + bi) - (c + di) = (a - c) + (b - d)i
4. Multiplication of Complex Numbers
   1. (a + bi) × (c + di) = (ac - bd) + (ad - bc)i
5. Multiplication Conjugates
   1. (a + bi)(a + bi) = a² + b²
6. Division of Complex Numbers
   1. 
7. Powers of Complex Numbers

1. iⁿ= i, if n = 4^a+1, i.e. one more than the multiple of 4.

Solved example based on Complex Number Formula

Example:

i¹ = i; i⁵ = i;i⁹ = i; i ^{4a + 1;}

2. iⁿ= -1, if n = 4a+2, i.e. two more than the multiple of 4.

Example:

i² = -1; i⁶ = -1; i^{10 = -1;i4a + 2}

3. iⁿ= -i, if n = 4^a+3, i.e. three more than the multiple of 4.

Example:

4. iⁿ= 1, if n = 4a, i.e. the multiple of 4. To get all the Maths formulas check out the main page. 

Pdf of Complex Number Formula