Kenneth S. answered • 12/07/16

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Zachariah C.

asked • 12/07/16Find the quotient of the complex numbers:

2*(sqrt 3)(cos(116 deg)+isin(116 deg))/2(cos(82 deg)+isin(82 deg))

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Kenneth S. answered • 12/07/16

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Charles B. answered • 12/07/16

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I think that what makes this one a bit tricky is that is looks complex. But if we use Euler's Equation, we can make this into a much simpler expression. Have you studied Euler yet? (It's pronounced "oiler"... maybe you remember your teacher mentioning this?)

according to Euler, cos(166^{ο}) + *i*sin(166^{ο}) = *e*^{166deg}*^{i}

similarly the bottom part can convert to e^{82deg}*^{i}

so the whole thing converts to :

2√3 e^{166deg*i}

2 e^{82deg*i}

The 2's cancel. Then we can combine the exponents of '*e*'.

166-82 = 84

√3 e^{84deg}*^{i}

your teacher MAY want that back in polar form. Do you know how to do Euler's formula in reverse, now that we've done it forwards?

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