The correct option is B 1/5+3/5i. ( 1+i )^2/3 i= 1+i^2+2i/3 i= 2i ( 3+i )/3^2 i^2 = 2 ( 3i+i^2 )/10= 1/5 ( 3i 1 )= 1/5+3/5i. Ans: B ...

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Logarithmic Differentiation

1+i 2/3-i

Question

$\frac{{(1 + i)}^{2}}{3 - i}$

\frac{1}{5} - \frac{3}{5} i .

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- \frac{1}{5} + \frac{3}{5} i .

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\frac{1}{4} - \frac{3}{4} i .

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- \frac{1}{4} + \frac{3}{4} i .

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Solution

The correct option is B $- \frac{1}{5} + \frac{3}{5} i .$
$\frac{{(1 + i)}^{2}}{3 - i} = \frac{1 + i^{2} + 2 i}{3 - i} = \frac{2 i (3 + i)}{3^{2} - i^{2}}$
$= \frac{2 (3 i + i^{2})}{10} = \frac{1}{5} (3 i - 1) = - \frac{1}{5} + \frac{3}{5} i .$
Ans: B

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