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Logarithmic Differentiation

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Question

Write $(i^{25})^{3}$ in polar form.

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Solution

$(i^{25})^{3} = i^{75} = i^{72 + 3} = (i^{72}) (i^{3}) = (i^{4})^{18} \cdot i^{3} = i^{3} = i^{2} \cdot i = - i$
$= i sin (- \frac{π}{2})$

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Q. The polar form of (i²⁵)³ is ____________.

Q. What is the polar form of the complex number

(i^{25})^{3}

Q. The polar form of (i²⁵)³ is
(a)

\cos \frac{π}{2} + i \sin \frac{π}{2}

(b) cos π + i sin π
(c) cos π − i sin π
(d)

\cos \frac{π}{2} - i \sin \frac{π}{2}

The polar form of $(i^{25})^{3}$ is

Write $(i^{25})$ in polar form.

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