All skills › Year 12 › Counting & Number
Year 12 · Counting & Number
Modulus and argument of complex numbers
A complex number has a real part and an imaginary part: a + bi, where i² = −1.
How to do it
- Add or subtract: combine real parts and imaginary parts separately.
- Multiply: expand like brackets and replace i² with −1.
- Modulus: √(a² + b²). Argument: the angle from the positive real axis.
Worked example
What is the modulus |z| of z = 2-2i?
|z| = √(re² + im²) = √(2² + -2²) = 2√2.
Answer: 2√2
With a free account, these play as step-by-step animations.
Watch outi² is −1, not 1.
Practise Modulus and argument of complex numbers properly
Ten-question rounds with instant marking, a lesson under every question, stars and badges. Free to start, and the first week includes Premium.
Create a free account
More Counting & Number skills