A) \[{{2}^{7}}\]
B) \[{{2}^{7}}i\]
C) \[{{2}^{14}}i\]
D) \[-{{2}^{7}}i\]
E) \[-{{2}^{14}}\]
Correct Answer: D
Solution :
\[z=\frac{7-i}{3-4i}\times \frac{3+4i}{3+4i}\]=\[\frac{21+25i+4}{16+9}=\frac{25\,(1+i)}{25}\] = \[(1+i)\] \[{{z}^{14}}={{(1+i)}^{14}}={{[{{(1+i)}^{2}}]}^{7}}\]= \[{{(2i)}^{7}}={{2}^{7}}{{i}^{7}}=-{{2}^{7}}i\].
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