====== 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.

===== Question 1 =====
 Chose the correct option.
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i.     ${{\left( \dfrac{2i}{1+i} \right)}^{2}}$ 
    * (a) $i$  
    * (b) $2i$
    * %%(c)%% $1-i$
    * (d) $i+1$ \\ <btn type="link" collapse="a1">See Answer</btn><collapse id="a1" collapsed="true">(B): $2i$</collapse>

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) $\dfrac{26}{7}+\dfrac{23}{7}i$  \\ <btn type="link" collapse="a2">See Answer</btn><collapse id="a2" collapsed="true">(C): $\dfrac{14}{25}+\dfrac{23}{25}i$</collapse>

iii. ${{i}^{57}}+\frac{1}{{{i}^{25}}}$, when simplified has the value  
    * (a) $0$ 
    * (b) $2i$
    * %%(c)%% $-2i$
    * (d) $2$  \\ <btn type="link" collapse="a3">See Answer</btn><collapse id="a3" collapsed="true">(A): $0$</collapse>

iv. 1+{i}^{2}+{i}^{4}+{i}^{6}+...+{i}^{2n}$  is  
    * (a) positive 
    * (b) negative
    * %%(c)%% $0$ 
    * (d) cannot be determined \\ <btn type="link" collapse="a4">See Answer</btn><collapse id="a4" collapsed="true">(D): cannot be determined </collapse>

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 \\ <btn type="link" collapse="a5">See Answer</btn><collapse id="a5" collapsed="true">(C): $y=5$</collapse>

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) $\dfrac{1}{4}\left( 3-2i \right)$ \\ <btn type="link" collapse="a6">See Answer</btn><collapse id="a6" collapsed="true">(B): $\dfrac{1}{13}\left( 3+2i \right)$</collapse>

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) $x=\dfrac{5}{13},y=-\dfrac{14}{13}$ \\ <btn type="link" collapse="a7">See Answer</btn><collapse id="a7" collapsed="true">(B): $x=\dfrac{5}{13},y=\dfrac{14}{13}$</collapse>

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<text align="right"><btn type="success">[[fsc-part1-kpk:sol:unit01:review-ex-1-p2|Question 2 & 3 >]]</btn></text>