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

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 √( ...

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Standard XII

Mathematics

Equality of 2 Complex Numbers

If a complex ...

Question

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

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\frac{1}{210}

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None

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Solution

The correct option is A 0
$z = \frac{20}{\sqrt{3} - \sqrt{2} i} + \frac{30}{- 2 \sqrt{3} + 3 \sqrt{2} i} - \frac{14}{2 \sqrt{3} - \sqrt{2} i}$
$= \frac{20 (\sqrt{3} + \sqrt{2} i)}{(\sqrt{3})^{2} - (\sqrt{2} i)^{2})} + \frac{30 (- 2 \sqrt{3} - 3 \sqrt{2} i)}{(- 2 \sqrt{3})^{2} - (3 \sqrt{2} i)^{2}} - \frac{14 (2 \sqrt{3} + \sqrt{2} i)}{(2 \sqrt{3})^{2} - (\sqrt{2} i)^{2}}$
$= \frac{20 (\sqrt{3} + \sqrt{2} i)}{5} - \frac{30 (2 \sqrt{3} + 3 \sqrt{2} i)}{30} - \frac{142 \sqrt{3} + \sqrt{2} i)}{14}$
$= 4 \sqrt{3} + 4 \sqrt{2} i - 2 \sqrt{3} - 3 \sqrt{2} i - 2 \sqrt{3} - \sqrt{2} i = 0$

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