Math

Divide Complex Numbers Calculator

Divide two complex numbers (a + bi) ÷ (c + di).

Calculated Output

Real part 3

Imaginary part (i) -1

Formula: Multiply by the conjugate of the denominator

Step-by-Step Breakdown

1. Values used:

2. a = 4

3. b = 2 i

4. c = 1

5. d = 1 i

7. Real part = 3

8. Imaginary part = -1i

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The math behind it

(a+bi)/(c+di) = (a+bi)(c−di) ÷ (c² + d²), which makes the denominator a real number.

(4 + 2i) ÷ (1 + i) = 3 − i.

What is the conjugate?

The conjugate of c + di is c − di — same real part, opposite imaginary part.