complex numbers mcq (1 Viewer)

Masaken · Nov 28, 2022

not sure how you would do it? i tried doing e^i(theta) = x + iy but then i got stuck, thanks in advance

jimmysmith560 · Nov 28, 2022

Would the following working help?

Let $e^{i\theta }=\cos \theta +i\sin \theta$

$\therefore e^{i\theta }\pm 2=\cos \theta \pm 2+i\sin \theta$

$\therefore \left|e^{i\theta }\pm 2\right|=\sqrt{\left(\cos \theta \pm 2\right)^2+\sin ^2\theta }=\sqrt{5\pm 4\cos \theta }$

∴ The maximum value of $\sqrt{5-4\cos \theta }+\sqrt{5+4\cos \theta }$ is $2\sqrt{5}$ , which occurs when $\theta =\frac{\pi }{2}\text{ or }\frac{3\pi }{2}$ .

The answer is therefore (C).

complex numbers mcq (1 Viewer)

Masaken

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jimmysmith560

Le Phénix Trilingue

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