# Question 1, Review Exercise

Solutions of Question 1 of Review Exercise of Unit 01: Complex Numbers. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan.

Chose the correct option.

i. Every real number is also a number.

• (a) natural
• (b) integer
• (c) complex
• (d) rational
(c): complex

ii. Every complex number has $\operatorname{part}(\mathrm{s})$.

• (a) one
• (b) two
• (c) three
• (d) no
(b): two

iii. Magnitude of a complex number $z$ is the distance of $z$ from

• (a) $(0,0)$
• (b)$(1,0)$
• (c) $(0,1)$
• (d) $(1,1)$
(a): $(0,0)$

iv. If $z$ is a complex number then its mirror image is

• (a) $|z|$
• (b) $1 / z$
• (c) $-z$
• (d) $\bar{z}$
(d): $\bar{z}$

v. In complex plane imaginary part is drawn along

• (a) $x$-axis
• (b) $y$-axis
• (c) origin
• (d) $x y$-plane
(b): $y$-axis

vi. If $z_{1}=3+2 i$ and $z_{2}=5+6 i$ then

• (a) $z_{1}>z_{2}$
• (b) $z_{1}<z_{2}$
• (c) $\overline{z_{1}}=\overline{z_{2}}$
• (d) $\overline{z_{1}}=-\overline{z_{2}}$
(d): $\overline{z_{1}}=-\overline{z_{2}}$

vii. Diagram representing a complex number is called diagram.

• (a) vector
• (b) Venn
• (c) argand
• (d) ordered pair
(c): argand

viii. If $\mathrm{z}=3+4 i$ then $\mathrm{z}^{-1}$ is

• (a) $\left(\frac{1}{3}, \frac{1}{4}\right)$
• (b) $\left(-\frac{1}{3},-\frac{1}{4}\right)$
• (c) $\left(\frac{3}{25}, \frac{-4}{25}\right)$
• (d) $\left(\frac{3}{25}, \frac{-4}{25}\right)$
(d): $\left(\frac{3}{25}, \frac{-4}{25}\right)$

ix. The value of $(\sqrt{-25})(\sqrt{-4})$ is

• (a) $10$
• (b) $-10$
• (c) $10 i$
• (d) $-10 i$
(b): $-10$

x. If $\left(\frac{1+i}{1-i}\right)^{n}=1$ then least positive value of $n$ is

• (a) $1$
• (b) $2$
• (c) $3$
• (d) $4$
<collapse id=“a10” collapsed=“true”>(b): $2$</collapse