Math Formulas: Complex numbers

Definitions:

A complex number is written as a + bi where a and b are real numbers an i, called the imaginary unit, has the property that i² = -1.

The complex numbers a + bi and a - bi are called complex conjugate of each other.

Formulas:

1) Equality of complex numbers

a + bi = c + di if and only if a = c and b = d

2) Addition of complex numbers

(a + bi) + (c + di) = (a + c) + (b + d)i

3) Subtraction of complex numbers

(a + bi) - (c + di) = (a - c) + (b - d)i

4) Multiplication of complex numbers

(a + bi)(c + di) = (ac - bd) + (ad + bc)i

5) Division of complex numbers

6) Polar form of complex numbers

7) Multiplication and division of complex numbers in polar form

8) De Moivre’s theorem

9) Roots of complex numbers

From this the n nth roots can be obtained by putting k = 0, 1, 2, . . ., n - 1