Question

( 3+i2/2-3i )+ ( 3-i2/2+i3 )
$( \frac{3 + i2}{2 - 3i}) +( \frac{3 - i2}{2 + i3} )$
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Answer 1

Step-by-step explanation:

We have,

$\dfrac{3 + 2i}{2 - 3i} + \dfrac{3 - 2i}{2 + 3i}$

$= \dfrac{(3 + 2i)(2 + 3i) + (3 - 2i)(2 - 3i)}{(2 - 3i)(2 + 3i)}$

$= \dfrac{6 + 4i + 9i + 6 {i}^{2} +6 - 4i - 9i + 6 {i}^{2} }{(2 - 3i)(2 + 3i)}$

$= \dfrac{6 +13i - 6 +6 - 13i - 6 }{(2 - 3i)(2 + 3i)}$

$= 0$