Question 1, Review Exercise 1

Solutions of Question 1 of Review Exercise 1 of Unit 01: Complex Numbers. This is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan.

Chose the correct option.

i. ${{\left( \dfrac{2i}{1+i} \right)}^{2}}$

  • (a) $i$
  • (b) $2i$
  • (c) $1-i$
  • (d) $i+1$
    See Answer
    (B): $2i$

ii. Divide $\dfrac{5+2i}{4-3i}$

  • (a) $-\dfrac{7}{25}+\dfrac{26}{25}i$
  • (b) $\dfrac{5}{4}-\dfrac{2}{3}i$
  • (c) $\dfrac{14}{25}+\dfrac{23}{25}i$
  • (d) $\dfrac{26}{7}+\dfrac{23}{7}i$
    See Answer
    (C): $\dfrac{14}{25}+\dfrac{23}{25}i$

iii. ${{i}^{57}}+\frac{1}{{{i}^{25}}}$, when simplified has the value

  • (a) $0$
  • (b) $2i$
  • (c) $-2i$
  • (d) $2$
    See Answer
    (A): $0$

iv. 1+{i}^{2}+{i}^{4}+{i}^{6}+…+{i}^{2n}$ is

  • (a) positive
  • (b) negative
  • (c) $0$
  • (d) cannot be determined
    See Answer
    (D): cannot be determined

v. If $z=x+iy$ and $|\dfrac{z-5i}{z+5i}|=1$, then $z$ lies on

  • (a) $X-axis$
  • (b) $Y-axis$
  • (c) line $y=5$
  • (d) None of these
    See Answer
    (C): $y=5$

vi. The multiplicative inverse of $z=3-2i$, is

  • (a) $\dfrac{1}{3}\left( 3+2i \right)$
  • (b) $\dfrac{1}{13}\left( 3+2i \right)$
  • (c) $\dfrac{1}{13}\left( 3-2i \right)$
  • (d) $\dfrac{1}{4}\left( 3-2i \right)$
    See Answer
    (B): $\dfrac{1}{13}\left( 3+2i \right)$

vii. If $\left( x+iy \right)\left( 2-3i \right)=4+i$, then

  • (a) $x=-\dfrac{14}{13},y=\dfrac{5}{13}$
  • (b) $x=\dfrac{5}{13},y=\dfrac{14}{13}$
  • (c) $x=\dfrac{14}{13},y=\dfrac{5}{13}$
  • (d) $x=\dfrac{5}{13},y=-\dfrac{14}{13}$
    See Answer
    (B): $x=\dfrac{5}{13},y=\dfrac{14}{13}$