How can you use trigonometric functions to simplify # 16 e^( ( 7 pi)/6 i ) # into a non-exponential complex number?

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How can you use trigonometric functions to simplify # 16 e^( ( 7 pi)/6 i ) # into a non-exponential complex number?

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Answer 1 · 2016-07-29T13:44:34

I used the exponential converion relationship:

Explanation:

You may remember that your complex number can be written as:
#z=rhoe^(thetai)=rho[cos(theta)+isin(theta)]#
in your case:
#z=16e^(7/6pii)=16[cos(7/6pi)+isin(7/6pi)]#
we can now evaluate the above trig functions and multiply by #16# to get to the form: #z=a+ib#:

#z=-13.8-8i#

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How can you use trigonometric functions to simplify # 16 e^( ( 7 pi)/6 i ) # into a non-exponential complex number?

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