Complex Numbers And Quadratic Equations question 844
Question: If $ z=\frac{7-i}{3-4i} $ then $ z^{14}= $ [Kerala (Engg.) 2005]
Options:
A) $ 2^{7} $
B) $ 2^{7}i $
C) $ 2^{14}i $
D) $ -2^{7}i $
Show Answer
Answer:
Correct Answer: C
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 $ .
BETA
