PLEASE HELP ME! Find the cube roots of 125(cos 288° + i sin 288°).

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25-07-2018
Mathematics

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PLEASE HELP ME! Find the cube roots of 125(cos 288° + i sin 288°).

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1rstar 1rstar · Answer 1 · 2018-07-25T18:45:18+02:00

◆ COMPLEX NUMBERS ◆

125 ( cos 288 + i sin 288 ) can be written as -

125.e^i( 288)
125.e^i( 288 +360 )
125.e^i( 288+ 720)

[ As , multiples of 360 can be added to an angle without changing any trigonometric functions or sign ]

To find the cube root , take the cube root of above 3 expressions ,

We get -
5 e^( i 96 )
5 e^( i 216 )
5 e^( i 336 )

Now using Euler's formula , We rewrite above as -

5 ( cos 96 + i sin 96 )
5(c os 216 + i sin 216 )
5 ( cos 336 + i sin 336 ) Ans.