Vidaara.orgClass 11 · Mathematics
CodeVID-M11-04-CT
Complex Numbers and Quadratic Equations — Full Chapter Test
Name: ____________________
Roll No.: __________
Date: ____________
General Instructions
- This is a full-length test covering the whole chapter — every topic is included.
- All questions are compulsory.
- Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
- Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions
5 × 1 = 5 marks
1.
$i^2=$
- A.$1$
- B.$-1$
- C.$i$
- D.$0$
2.
$|3+4i|=$
- A.$5$
- B.$7$
- C.$1$
- D.$25$
3.
The roots of $x^2+4=0$ are:
- A.$\pm2$
- B.$\pm2i$
- C.$\pm4i$
- D.$\pm4$
4.
$i^3=$
- A.$i$
- B.$-i$
- C.$1$
- D.$-1$
5.
The conjugate of $7+2i$ is:
- A.$7-2i$
- B.$-7+2i$
- C.$2+7i$
- D.$-7-2i$
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Simplify $(2+3i)-(1+i)$.
7.
Find $|1+i|$.
8.
Solve $x^2+9=0$.
9.
Find $i^{10}$.
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
Express $(1+i)^2$ in the form $a+bi$.
11.
Find the modulus and conjugate of $z=1-i$.
12.
Solve $x^2-2x+2=0$.
13.
Simplify $(3+2i)(3-2i)$.
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
If $z_1=2+3i$ and $z_2=1-2i$, find $z_1+z_2,\ z_1-z_2$ and $z_1z_2$.
15.
Express $z=\dfrac{1+i}{1-i}$ in $a+bi$ form and find $|z|$ and $\arg z$.
Answer Key
Section A — Multiple Choice Questions
- (B) $-1$
- (A) $5$
- (B) $\pm2i$
- (B) $-i$
- (A) $7-2i$
Section B — Short Answer (2 marks)
- $1+2i$.
- $\sqrt2$.
- $x=\pm3i$.
- $-1$.
Section C — Short Answer (3 marks)
- $2i$.
- $|z|=\sqrt2$, $\bar z=1+i$.
- $x=1\pm i$.
- $13$.
Section D — Long Answer (5 marks)
- $z_1+z_2=3+i$; $z_1-z_2=1+5i$; $z_1z_2=8-i$.
- $z=i$; $|z|=1$, $\arg z=\tfrac{\pi}{2}$.
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