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): $x=\dfrac{5}{13},y=\dfrac{14}{13}$