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

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Answer 1 · 2017-08-15T16:45:38

#3/4 - (3sqrt3)/4i#

I'll assume the trigonometric arguments are in degrees.

We're asked to find the standard form of

#3/2(cos[300^"o"] + isin[300^"o"])#

Well, #cos[300^"o"] = cos[-60^"o"] = color(red)(1/2#

And #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" ")|)#