Discussion Forum



1)

If $Z= \frac{7-i}{3-4i}$ , then z14 = 


A) $2^{7}$

B) $2^{7}i$

C) $2^{14}i$

D) $-2^{7}i$

Answer:

Option D

Explanation:

$Z= \frac{7-i}{3-4i}\times\frac{3+4i}{3+4i}$

$\frac{21+25i+4}{16+9}=\frac{25(1+i)}{25}=(1+i)$

$z^{14} = (1+i)^{14} = \left[\left(1+i\right)^{2}\right]^{7}=(2i)^{7}$

= $2^{7}i^{7} = -2^{7}i$