Question -
Answer -
Given: Z = (i25)3
= i75
= i74. i
= (i2)37.i
= (-1)37. i
= (-1). i
= – i
= 0 – i
So now,
|Z| = √(x2 + y2)
= √(02 + (-1)2)
= √(0 + 1)
= √1
θ = tan-1 (|y|/ |x|)
= tan-1 (1/ 0)
= tan-1 ∞
Since x ≥ 0, y < 0complex number lies in 4th quadrant and the value of θ is -900≤θ≤00.
θ = -π/2
Z = 1 (cos (-π/2) + isin (-π/2))
= 1 (cos (π/2) – i sin(π/2))
∴ Polar form of (i25)3 is1 (cos (π/2) – i sin (π/2))