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
  <btn type=“link” collapse=“a1”>See Answer</btn>

  (c): complex

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

• (a) one
• (b) two
• (c) three
• (d) no
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  (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) $(1,1)$
  <btn type=“link” collapse=“a3”>See Answer</btn>

  (a): $(0,0)$

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

• (a) $|z|$
• (b) $1 / z$
• (c) $-z$
• (d) $\bar{z}$
  <btn type=“link” collapse=“a4”>See Answer</btn>

  (d): $\bar{z}$

v. In complex plane imaginary part is drawn along

• (a) $x$-axis
• (b) $y$-axis
• (c) origin
• (d) $x y$-plane
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  (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) $\overline{z_{1}}=-\overline{z_{2}}$
  <btn type=“link” collapse=“a6”>See Answer</btn>

  (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
  <btn type=“link” collapse=“a7”>See Answer</btn>

  (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) $\left(\frac{3}{25}, \frac{-4}{25}\right)$
  <btn type=“link” collapse=“a8”>See Answer</btn>

  (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) $-10 i$
  <btn type=“link” collapse=“a9”>See Answer</btn>

  (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) $4$
  <btn type=“link” collapse=“a10”>See Answer</btn><collapse id="a10" collapsed="true">%%(b)%%: $2$</collapse ====Go to ==== <text align="right"><btn type="success">[[math-11-nbf:sol:unit01:Re-ex-p2|Question 2 >]]</btn></text>