The conjugate of ( 2 + i ) 2 3 + i , in the form of a+ib, is Options: A . &nbsp 13 2 + i ( 15 2 ) B . &nbsp 13 10 + i ( − 15 2 ) C . &nbsp 13 10 + i ( − 9 10 ) D . &nbsp 13 10 + i ( 9 10 )

Answer: Option C : C z = ( 2 + i ) 2 3 + i = 3 + 4 i 3 + i × 3 − i 3 − i = 13 10 + i 9 10 Conjugate = 13 10 − i 9 10 .

The conjugate of (2+i)23+i , in the form of a+ib, is

Question

The conjugate of $\frac{(2 + i)^{2}}{3 + i}$ , in the form of a+ib, is

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})

Answer: Option C
:
C

z = $\frac{(2 + i)^{2}}{3 + i} = \frac{3 + 4 i}{3 + i} \times \frac{3 - i}{3 - i} = \frac{13}{10} + i \frac{9}{10}$

Conjugate = $\frac{13}{10} - i \frac{9}{10}$ .

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