Formulas of Complex Numbers

Formulas of Complex Numbers

Definition :

i = √-1 and i2 = -1, i3 = i.i = -i,

i4 = i3 . i = -i . i = 1,…i4n = 1,
i4n+1 = 1, i4n+2 = -1, i4n+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 + bdi2 = (ac – bd) + (ad + bc)i

Multiplying Conjugates : (a + bi)(a – bi) = A2 + b2

Division : a + bi / c + di = a + bi / c + di x c – di / c – di = ac + bd / c2 + d2 + (bc – ad / c2 + d2)i

 

 

 

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