What is the polar form of the complex number (i25)3 ?

Question

What is the polar form of the complex number (i25)3 ? (A) cos (π/3)-isin (π/3) (B) (cos(-(π/2))+i sin(-(π/2))) (C) cos (π/4)+ i sin (π/4) (D) (cos(π/2)+i sin (π/2))

Tardigrade Admin · Accepted Answer

Let z =(i25)3 =(i)75 =i4×18+3=(i4)18(i)3 =i3=-i=0-i Polar form of z = r (cos θ+isin θ) =1 cos(-(π/2))+i sin (-(π/2)) =cos (π/2)-i sin (π/2)

Q. What is the polar form of the complex number $(i^{25})^{3}$ ?

$cos \frac{π}{3} - i s in \frac{π}{3}$

$(cos (- \frac{π}{2}) + i s in (- \frac{π}{2}))$

$cos \frac{π}{4} + i s in \frac{π}{4}$

$(cos \frac{π}{2} + i s in \frac{π}{2})$

Let $z = (i^{25})^{3} = (i)^{75}$
$= i^{4 \times 18 + 3} = (i^{4})^{18} (i)^{3}$
$= i^{3} = - i = 0 - i$
Polar form of $z = r (cos θ + i s in θ)$
$= 1 {cos (- \frac{π}{2}) + i s in (- \frac{π}{2})}$
$= cos \frac{π}{2} - i s in \frac{π}{2}$

Q. What is the polar form of the complex number (i25)3 ?

cos3π​−isin3π​

(cos(−2π​)+isin(−2π​))

cos4π​+isin4π​

(cos2π​+isin2π​)