Dividing Complex Numbers by Complex Numbers

Addition and multiplication of complex numbers is straightforward. If you divide by a real number it is easy: divide real and non real parts by the number, for example: (2 + 6i)/2 = 1 + 3i.

Division by a non-real number takes a little more work. The trick is to turn division into multiplication, using the complex conjugate.

Example: (2 + 3i) / (1 – i)

Multiply numerator and denominator by the complex conjugate of 1 – i, which is 1 + i:

(2 + 3i) x (1 + i ) = 2 – 3 + 3i + i = -1 + 4i

(1 – i) x (1 + i) = 1 – i + i + 1 = 2

Solution: (-1 + 4i)/2 = -1/2 + 2i

In the following problems, do the division.

1. 1 / i

(1 divided by i).

2. (2 + 3i)/i

3. (1 + i) / (1 – i)

4. i / (1 – i)

5. (3 – 2i) / (3 + 2i)