Operations on
Complex Numbers
Computation is less complex if you
know these rules.
i is for imaginary number. Its value is √-1
Addition
(a + bi) + (c + di) = (a + c) + (b + d)i
Get the sum of the Get the sum of the
real numbers. imaginary numbers.
Subtraction
(a + bi) - (c + di) = (a - c) + (b - d)i
Subtract the real Subtract the
numbers. imaginary numbers.
Multiplication
Use FOIL method then combine like terms.
(a + bi)(c + di) = (ac-bd) + (ad+bc)i
First, Outer, Inner, and Last, (FOIL)
bi⋅di = bd i2 = bd (√-1)2
= bd (-1) = –bd
Division
(a + bi) (a + bi) (c - di) (ac+bd) + (bc-ad)i
(c + di) = (c + di) · (c - di) =
c2 + d2
Multiply both the numerator and the Simplify.
denominator by the conjugate of the
denominator.
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