ECAT Mathematics — Complex Numbers
Complex Numbers is part of the Mathematics section of the UET ECAT (30 of the 100 MCQs). It breaks into 5 subtopics, and we hold 28 ECAT-pattern practice MCQs on it, each with a written explanation. Tap a subtopic below to practise just that.
Subtopics (5)
How Complex Numbers is tested
Across the 7 ECAT past papers on ParhaiKrlo, Complex Numbers accounts for 8 questions. It appears in 6 of them, about 1.3 questions a paper. The heaviest was ECAT Past Paper 02, with 3 questions, and the most recent is ECAT Past Paper 07, with 1.
| Paper | Questions |
|---|---|
| ECAT Past Paper 07 | 1 |
| ECAT Past Paper 06 | 1 |
| ECAT Past Paper 05 | 1 |
| ECAT Past Paper 03 | 1 |
| ECAT Past Paper 02 | 3 |
| ECAT Past Paper 01 | 1 |
Complex Numbers MCQs from the ECAT past papers
Try each one before opening the answer. Each comes with a short explanation.
- Q1 · ECAT Past Paper 07 · Complex Numbers
The additive inverse of 3 − i, where i = √−1, is:
- A.−3 + i
- B.3 − i
- C.−3 − i
- D.3 + i
Show answer
Answer: A. −3 + i — −(3 − i) = −3 + i.
- Q2 · ECAT Past Paper 06 · Complex Numbers
The complex number 1 + i can be expressed as:
- A.2(cos 60° + i sin 30°)
- B.√2(cos 45° + i sin 45°)
- C.cos 60° + i sin 60°
- D.√2(cos 30° + i sin 30°)
Show answer
Answer: B. √2(cos 45° + i sin 45°) — |1 + i| = √2 and arg(1 + i) = 45°.
- Q3 · ECAT Past Paper 05 · Complex Numbers
The complex number 1 + i√3 can be expressed as:
- A.2(cos 30° + i sin 30°)
- B.cos 60° + i sin 60°
- C.2(cos 60° + i sin 60°)
- D.sin 30° + i cos 30°
Show answer
Answer: C. 2(cos 60° + i sin 60°) — Modulus √(1 + 3) = 2; argument tan⁻¹(√3) = 60°.