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Question #ed5b1

1 Answer

May 25, 2017

$\frac{1}{26} + (\frac{5}{26}) i .$ $1/26+(5/26)i.$

Explanation:

Let, $z = \frac{i}{5 + i} .$ $z=i/(5+i).$

$\Rightarrow z = \frac{i}{5 + i} \times \frac{5 - i}{5 - i},$ $rArr z=i/(5+i)xx(5-i)/(5-i),$

$= \frac{5 i - i^{2}}{5^{2} - i^{2}},$ $=(5i-i^2)/(5^2-i^2),$

$= \frac{5 i - (- 1)}{25 - (- 1)},$ $=(5i-(-1))/(25-(-1)),$

$= \frac{1 + 5 i}{26},$ $=(1+5i)/26,$

$:. z=1/26+(5/26)i.$

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