## Formulas of Complex Numbers

### Definition:

i = √-1 and i^{2} = -1, i^{3} = i^{2 }.i = -i,

i^{4} = i^{3} . i = -i . i = 1,…i^{4n} = 1,

i^{4n+1} = 1, i^{4n+2} = -1, i^{4n+3} = -i

**Complex number is any number of the form a + bi and where as a and b are real number.**

**Addition:** (a + bi) + (c + di) = (a + c) + (b + d)i

**Subtraction :** (a + bi) – (c + di) = (a – c) + (b – d)i

**Multiplication :**(a + bi)(c + di) = ac + adi + bci + bdi^{2} = (ac – bd) + (ad + bc)i

**Multiplying Conjugates :** (a + bi)(a – bi) = A^{2} + b^{2}

**Division :** a + bi / c + di = a + bi / c + di x c – di / c – di = ac + bd / c^{2} + d^{2} + (bc – ad / c^{2} + d^{2})i

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