If a complex number then -z- would bez- 20-3- -2-303-2-2-3-142-3 - -2

Z=20√(3) √(2)i+30 2√(3)+3√(2)i 142√(3) √(2)i =20(√(3)+√(2)i)(√(3))^2 (√(2)i)^2+30( 2√(3) 3√(2)i)( 2√(3))^2 (3√(2)i)^2 14(2√(3)+√(2)i)(2√(3))^2 (√(2)i)^2 =20(√ ...

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Engineering Mathematics

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If a complex ...

Question

If a complex number then |z| would be
$z = \frac{20}{\sqrt{3} - \sqrt{- 2}} + \frac{30}{3 \sqrt{- 2} - 2 \sqrt{3}} - \frac{14}{2 \sqrt{3} - \sqrt{- 2}}$

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Solution

The correct option is A 0
$z = \frac{20}{\sqrt{3} - \sqrt{2} i} + \frac{30}{- 2 \sqrt{3} + 3 \sqrt{2} i} - \frac{14}{2 \sqrt{3} - \sqrt{2} i}$

$= \frac{20 (\sqrt{3} + \sqrt{2} i)}{(\sqrt{3})^{2} - (\sqrt{2} i)^{2}} + \frac{30 (- 2 \sqrt{3} - 3 \sqrt{2} i)}{(- 2 \sqrt{3})^{2} - (3 \sqrt{2} i)^{2}} - \frac{14 (2 \sqrt{3} + \sqrt{2} i)}{(2 \sqrt{3})^{2} - (\sqrt{2} i)^{2}}$

$= \frac{20 (\sqrt{3} + \sqrt{2} i)}{5} - \frac{30 (2 \sqrt{3} + 3 \sqrt{2} i)}{30} - \frac{14 (2 \sqrt{3} + \sqrt{2} i)}{14}$

$= 4 \sqrt{3} + 4 \sqrt{2} i - 2 \sqrt{3} - 3 \sqrt{2} i - 2 \sqrt{3} - \sqrt{2} i = 0$

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If a complex number then |z| would be z=20√3−√−2+303√−2−2√3−142√3−√−2

If a complex number then |z| would be
$z = \frac{20}{\sqrt{3} - \sqrt{- 2}} + \frac{30}{3 \sqrt{- 2} - 2 \sqrt{3}} - \frac{14}{2 \sqrt{3} - \sqrt{- 2}}$