Question

Find the cube roots of 125i, using the method of finding nth cube roots.... I need help in knowing how to tell what the angle is.

Answer 1

since on the complex plane maginary no are either on positive y axix or negative y axis
depends on the sign of imaginary part .since 125i is posive and has real part zero so it will be along imaginary axis (along positive y axis )
the angle corresponding to this must be pi/2 .

Answer 2

@sami-21: Excuse me, can you explain me clearer. I have problem with this, too. and, if we scale the y axis, I mean the imaginary part, which point can we represent that number

Answer 3

ok let me try

Answer 4

my problem is with the formula we have to use, see to me an angle of pi/2 implies that there would be 4 cube roots while clearly there is 3 cube roots

Answer 5

@Edutopia you mean it must be cube roots, so is it 2pi/3

Answer 6

not nessicarly...

Answer 7

you can see on the y axis (which is called imaginary axis is correcponding to the angle 90 or pi/2 ) . no matter what is the constant factor if its pure positive imaginary there angle will be pi/2 for example

i , 5i ,40i, 50i, 70i,90, 150i, 125i , all have angle of pi/2 .
while all the following (negative )

-i,-5i,-20i,-30i-100i, -125i .......... all have angle of -pi/2 .