# 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) $i+1$
(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) $\dfrac{26}{7}+\dfrac{23}{7}i$
(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) $2$
(A): $0$

iv. 1+{i}^{2}+{i}^{4}+{i}^{6}+…+{i}^{2n}$is • (a) positive • (b) negative • (c)$0$• (d) cannot be determined (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 (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)$\dfrac{1}{4}\left( 3-2i \right)$(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)$x=\dfrac{5}{13},y=-\dfrac{14}{13}$(B):$x=\dfrac{5}{13},y=\dfrac{14}{13}\$