Let Z=√(2+3i)√(2 3i) =√(2+3i)√(2 3i)×√(2+3i)√(2+3i) =2+3i√(4 9i^2) =2+3i√(4+9) ∴ Z=2√(13)+i3√(13) ...

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Complex Numbers

Simplify: √2...

Question

Simplify: $\frac{\sqrt{2 + 3 i}}{\sqrt{2 - 3 i}}$

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Solution

Let $Z = \frac{\sqrt{2 + 3 i}}{\sqrt{2 - 3 i}}$

$= \frac{\sqrt{2 + 3 i}}{\sqrt{2 - 3 i}} \times \frac{\sqrt{2 + 3 i}}{\sqrt{2 + 3 i}}$

$= \frac{2 + 3 i}{\sqrt{4 - 9 i^{2}}}$

$= \frac{2 + 3 i}{\sqrt{4 + 9}}$

$∴ Z = \frac{2}{\sqrt{13}} + i \frac{3}{\sqrt{13}}$

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