The correct option is A 2√(3)+2i 20e^i19π185e^i2π/9 4e^i[(19π/18) (2π/9)] 4e^i[(15× 180)/18] 4e^i× 150^∘ 2√(3) +2i ...

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20cis19π185ci...

Question

$\frac{20 c i s (\frac{19 π}{18})}{5 c i s (\frac{2 π}{9})} =$

- 2 \sqrt{3} + 2 i

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- 2 \sqrt{3} - 2 i

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2 \sqrt{3} + 2 i

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- 2 + 2 i \sqrt{3}

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- 2 - 2 i \sqrt{3}

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Solution

The correct option is A $2 \sqrt{3} + 2 i$
$\frac{20 e^{i \frac{19 π}{18}}}{5 e^{i 2 π / 9}}$
$⟹ 4 e^{i [(19 π / 18) - (2 π / 9)]}$
$⟹ 4 e^{i [(15 \times 180) / 18]}$
$⟹ 4 e^{i \times 150^{\circ}}$
$⟹ 2 \sqrt{3} + 2 i$

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