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

Answer:

Explanation:

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

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

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

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