Divide Complex Numbers Calculator
Divide a + bi by c + di and read the real part and imaginary coefficient.
Formula
(a+bi)/(c+di) = (ac+bd)/(c²+d²) + [(bc−ad)/(c²+d²)]i
Real part ≈ ((3)×(1)+(4)×(-2))÷((1)^2+(-2)^2) · Imaginary coefficient ≈ ((4)×(1)-(3)×(-2))÷((1)^2+(-2)^2)
How to use
- Enter a and b for the numerator.
- Enter c and d for the nonzero denominator.
- Combine the results as real + imaginary × i.
Examples
- (3 + 4i)/(1 − 2i) = −1 + 2i.
Frequently asked questions
May c or d be zero?
Yes, but they cannot both be zero.
Why use the conjugate?
Multiplying by c−di makes the denominator c²+d² real.
Are the results exact?
Decimal outputs are rounded; exact rational coefficients may repeat.
Sources
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