Question

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

Answer 1

◆ 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.