Complex numbers (NF)
A standard method from Quadratic equations in one unknown: the steps and worked examples.
Steps
- i² = −1.
- Add and multiply like algebra, then replace i² by −1.
- Divide: multiply the top and bottom by the conjugate of the bottom (a + bi → a − bi).
Want to check an answer? Quadratic equation calculator shows every step.
Worked examples
Example 1: Complex numbers (NF): work out (3 + 2i)(1 − i) and (2 + i)/(1 − 2i).
(3 + 2i)(1 − i) = 3 − 3i + 2i − 2i² = 5 − i
(2 + i)(1 + 2i) / [(1 − 2i)(1 + 2i)]
= (2 + 5i + 2i²) / 5
= 5i / 5
= iFor the whole topic, read Quadratic equations in one unknown: key points, common mistakes and how the DSE tests it.