(√(10))^20((3√(10)+i√(10))^20 (3√(10) i√(10))^20) cosθ = 3√(10) , sin = 1√(10) (√(10))^20× (cos20θ + isin20θ cos 20θ + isin20θ) (√(10)^2 ...

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Complex Numbers

Solve : 3+i2...

Question

Solve : $(3 + i)^{20} - (3 - i)^{20}$ .

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Solution

$(\sqrt{10})^{20} ((\frac{3}{\sqrt{10}} + \frac{i}{\sqrt{10}})^{20} - (\frac{3}{\sqrt{10}} - \frac{i}{\sqrt{10}})^{20})$
$cos θ = \frac{3}{\sqrt{10}}, sin = \frac{1}{\sqrt{10}}$
$(\sqrt{10})^{20} \times (cos 20 θ + i sin 20 θ - cos 20 θ + i sin 20 θ)$
$({\sqrt{10}}^{20}) (2 i sin 20 θ)$

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