Complex Numbers And Quadratic Equations question 51
Question: The conjugate of $ \frac{{{(2+i)}^{2}}}{3+i}, $ in the form of a + ib, is [Karnataka CET 2001; Pb. CET 2001]
Options:
A) $ \frac{13}{2}+i( \frac{15}{2} ) $
B) $ \frac{13}{10}+i( \frac{-15}{2} ) $
C) $ \frac{13}{10}+i( \frac{-9}{10} ) $
D) $ \frac{13}{10}+i( \frac{9}{10} ) $
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Answer:
Correct Answer: C
Solution:
$ z=\frac{{{(2+i)}^{2}}}{3+i} $ $ =\frac{3+4i}{3+i}\times \frac{3-i}{3-i} $ $ =\frac{13}{10}+i\frac{9}{10} $ Conjugate $ =\frac{13}{10}-i\frac{9}{10} $ .
BETA
