Question

evaluate: |(3-2i)/(3+2i) + (3+2i)/(3-2i)|​

Answer 1

SOLUTION

TO EVALUATE

$\displaystyle\sf{ \bigg| \: \frac{3 - 2i}{3 + 2i} + \frac{3 + 2i}{3 - 2i} \: \bigg| }$

EVALUATION

Here the given expression is

$\displaystyle\sf{ \bigg| \: \frac{3 - 2i}{3 + 2i} + \frac{3 + 2i}{3 - 2i} \: \bigg| }$

We simplify it as below

$\displaystyle\sf{ \bigg| \: \frac{3 - 2i}{3 + 2i} + \frac{3 + 2i}{3 - 2i} \: \bigg| }$

$\displaystyle\sf{ = \bigg| \: \frac{{(3 - 2i)}^{2} + {(3 + 2i)}^{2} }{(3 + 2i)(3 - 2i)} \: \bigg| }$

$\displaystyle\sf{ = \bigg| \: \frac{2{ \big[(3 )}^{2} + {(2i)}^{2} \big]}{( {3}^{2} ) - {(2i)}^{2} } \: \bigg| }$

$\displaystyle\sf{ = \bigg| \: \frac{2\big[ 9 + 4{i}^{2} \big]}{9 - 4 {i}^{2} } \: \bigg| }$

$\displaystyle\sf{ = \bigg| \: \frac{2\big[ 9 - 4 \big]}{9 + 4 } \: \bigg| }$

$\displaystyle\sf{ = \bigg| \: \frac{10}{13} \: \bigg| }$

$\displaystyle\sf{ = \: \frac{10}{13} \: }$

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Answer 2

Answer:

the smallest structural and functional unit of an organism, which is typically microscopic and consists of cytoplasm and a nucleus enclosed in a membrane.