Explanation

The complex conjugate of:
a + bi is a − bi

Multiplying a complex number by its conjugate removes i.

Example:
(3 + 4i)(3 − 4i) = 9 − 16i² = 25

Dividing complex numbers:
Multiply top and bottom by the conjugate of the denominator.

Example:
(2 + i)/(1 − i)

Multiply by (1 + i)/(1 + i).

Quiz

1. What is the conjugate of 5 − 2i?

2. What happens to i when multiplying by the conjugate?

3. Why do we use conjugates when dividing?

4. Is the conjugate a reflection across an axis?

5. Does the conjugate change the real part?

Answer Key

1. 5 + 2i

2. It disappears

3. To remove i from the denominator

4. Yes, across the real axis

5. No