Example 1 · level 1
Simplify (4 + 2i) − (2 − 6i). Choose the answer in the form a + bi.
- 2 − 8i
- −2 + 8i
- 6 − 4i
- 2 + 8i
Show solution
- Real part: 4 − 2 = 2.
- Imaginary part: 2 − (−6) = 8.
- Answer: 2 + 8i.
Answer: 2 + 8i
CLASS 11 MATHS · COMPLEX NUMBERS
Complex number arithmetic and modulus
Add or subtract real and imaginary parts separately. To multiply, expand and use i² = −1. The modulus of a + bi is √(a² + b²).
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Worked examples
Example 2 · level 2
Find |z₁z₂| if z₁ = −24 − 7i and z₂ = 3 + 4i.
Show solution
- |z₁| = 25, |z₂| = 5.
- |z₁z₂| = 25 × 5 = 125.
Answer: 125
Example 3 · level 3
Simplify (1 − 6i)(−1 − 4i). Choose the answer in the form a + bi.
- −25 − 2i
- 25 + 2i
- −25 + 2i
- 23 + 2i
Show solution
- (1 − 6i)(−1 − 4i) = −1 − 4i + 6i + 24i².
- i² = −1, so 24i² = −24.
- Real: −1 − 24 = −25; imaginary: −4 + 6 = 2.
- Answer: −25 + 2i.
Answer: −25 + 2i