How do you write the complex number in standard form $\frac{3}{2} (cos 300 + i sin 300)$ $3/2(cos300+isin300)$ ?

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Answer 1 · 2017-08-15T16:45:38

$\frac{3}{4} - \frac{3 \sqrt{3}}{4} i$ $3/4 - (3sqrt3)/4i$

I'll assume the trigonometric arguments are in degrees.

We're asked to find the standard form of

$\frac{3}{2} (cos [300^{o}] + i sin [300^{o}])$ $3/2(cos[300^"o"] + isin[300^"o"])$

Well, $cos [300^{o}] = cos [- 60^{o}] = \frac{1}{2}$ $cos[300^"o"] = cos[-60^"o"] = color(red)(1/2$

And $sin [300^{o}] = sin [- 60^{o}] = - \frac{\sqrt{3}}{2}$ $sin[300^"o"] = sin[-60^"o"] = color(green)(-sqrt3/2$

So we have

$3/2(1/2 - (isqrt3)/2) = color(blue)(ulbar(|stackrel(" ")(" "3/4 - (3sqrt3)/4i" ")|)$

How do you write the complex number in standard form 3/2(cos300+isin300)32(cos300+isin300)3/2(cos300+isin300)?