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
  See Answer

  (c): complex

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

• (a) one
• (b) two
• (c) three
• (d) no
  See Answer

  (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) $(1,1)$
  See Answer

  (a): $(0,0)$

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

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

  (d): $\bar{z}$

v. In complex plane imaginary part is drawn along

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

  (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) $\overline{z_{1}}=-\overline{z_{2}}$
  See Answer

  (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
  See Answer

  (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) $\left(\frac{3}{25}, \frac{-4}{25}\right)$
  See Answer

  (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) $-10 i$
  See Answer

  (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) $4$
  See Answer<collapse id=“a10” collapsed=“true”>(b): $2$</collapse

Question 2 >