Question -
Answer -
Given: Z = (i25)3
= i75
= i74. i
= (i2)37.i
= (-1)37. i
= (-1). i
= тАУ i
= 0 тАУ i
So now,
|Z| =┬атИЪ(x2┬а+ y2)
=┬атИЪ(02┬а+ (-1)2)
=┬атИЪ(0 + 1)
=┬атИЪ1
╬╕ = tan-1┬а(|y|/ |x|)
= tan-1┬а(1/ 0)
= tan-1┬атИЮ
Since x тЙе 0, y < 0complex number lies in 4th┬аquadrant and the value of ╬╕ is -900тЙд╬╕тЙд00.
╬╕ = -╧А/2
Z = 1 (cos (-╧А/2) + isin (-╧А/2))
= 1 (cos (╧А/2) тАУ i sin(╧А/2))
тИ┤ Polar form of (i25)3┬аis1 (cos (╧А/2) тАУ i sin (╧А/2))