Vidaara.orgClass 11 · Mathematics
CodeVID-M11-04-MOD-01
Modulus, Conjugate & Argand Plane — 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.
$|3+4i|=$
- A.$5$
- B.$7$
- C.$1$
- D.$25$
2.
The conjugate of $7+2i$ is:
- A.$7-2i$
- B.$-7+2i$
- C.$2+7i$
- D.$-7-2i$
3.
$z\bar z$ equals:
- A.$|z|$
- B.$|z|^2$
- C.$z^2$
- D.$2|z|$
4.
$|-5i|=$
- A.$5$
- B.$-5$
- C.$25$
- D.$1$
5.
$\arg(i)=$
- A.$0$
- B.$\tfrac{\pi}{2}$
- C.$\pi$
- D.$\tfrac{\pi}{4}$
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Find $|1+i|$.
7.
Find the conjugate of $3-4i$.
8.
Find $|z|$ for $z=6-8i$.
9.
Express $\dfrac1i$ in the form $a+bi$.
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
Find the modulus and conjugate of $z=1-i$.
11.
Simplify $\dfrac{2+3i}{1-i}$ into $a+bi$ form.
12.
Find $\left|\dfrac{1+i}{1-i}\right|$.
13.
Find the argument of $-1+i$.
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
Express $z=\dfrac{1+i}{1-i}$ in $a+bi$ form and find $|z|$ and $\arg z$.
15.
Find the modulus and argument of $z=-\sqrt3+i$.
Answer Key
Section A — Multiple Choice Questions
- (A) $5$
- (A) $7-2i$
- (B) $|z|^2$
- (A) $5$
- (B) $\tfrac{\pi}{2}$
Section B — Short Answer (2 marks)
- $\sqrt2$.
- $3+4i$.
- $10$.
- $-i$.
Section C — Short Answer (3 marks)
- $|z|=\sqrt2$, $\bar z=1+i$.
- $-\tfrac12+\tfrac52 i$.
- $1$.
- $\tfrac{3\pi}{4}$.
Section D — Long Answer (5 marks)
- $z=i$; $|z|=1$, $\arg z=\tfrac{\pi}{2}$.
- $|z|=2$, $\arg z=\tfrac{5\pi}{6}$.
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