Vidaara.orgClass 11 · Mathematics
CodeVID-M11-04-CPX-01
Complex Numbers & Their Algebra — Assignment
Name: ____________________
Roll No.: __________
Date: ____________
General Instructions
- 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.
$i^3=$
- A.$i$
- B.$-i$
- C.$1$
- D.$-1$
3.
$(3+2i)+(1+4i)=$
- A.$4+6i$
- B.$4+2i$
- C.$2+6i$
- D.$4-6i$
4.
The real part of $5-7i$ is:
- A.$-7$
- B.$5$
- C.$7$
- D.$-5$
5.
$(2i)(3i)=$
- A.$6$
- B.$-6$
- C.$6i$
- D.$-6i$
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Simplify $(2+3i)-(1+i)$.
7.
Find $i^{10}$.
8.
Multiply $(1+i)(2-i)$.
9.
Find the real and imaginary parts of $4-3i$.
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
Express $(1+i)^2$ in the form $a+bi$.
11.
Simplify $(3+2i)(3-2i)$.
12.
Find $i+i^2+i^3+i^4$.
13.
Express $(1+i)^3$ in the form $a+bi$.
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.
Find the value of $(1+i)^4$.
Answer Key
Section A — Multiple Choice Questions
- (B) $-1$
- (B) $-i$
- (A) $4+6i$
- (B) $5$
- (B) $-6$
Section B — Short Answer (2 marks)
- $1+2i$.
- $-1$.
- $3+i$.
- Real $4$, imaginary $-3$.
Section C — Short Answer (3 marks)
- $2i$.
- $13$.
- $0$.
- $-2+2i$.
Section D — Long Answer (5 marks)
- $z_1+z_2=3+i$; $z_1-z_2=1+5i$; $z_1z_2=8-i$.
- $-4$.
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