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Question -

Write (i25)3┬аin polar form.



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))

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