Question

If i = $\sqrt{- 1}$ then 4 + 5$\left( - \frac{1}{2} + i\frac{\sqrt{3}}{2} \right)^{334}$–3$\left( \frac{1}{2} + i\frac{\sqrt{3}}{2} \right)^{365}$is equal to–

• A. 1 – i$\sqrt{3}$
• B. –1 + i$\sqrt{3}$
• C. 4$\sqrt{3}$I
• D. –i$\sqrt{3}$

Answer 1

Answer: (C)

4$\sqrt{3}$I

Answer 2

Sol. As, 4 + 5$\left( - \frac{1}{2} + \frac{i\sqrt{3}}{2} \right)^{334}$–3$\left( \frac{1}{2} + \frac{i\sqrt{3}}{2} \right)^{365}$

Ž 4 + 5(w)³³⁴ – 3 (w²)³⁶⁵

Ž 4 + 5w + 3w

Ž $\frac{1}{2}${8 – 5 + 5i$\sqrt{3}$ – 3 + 3i$\sqrt{3}$}

Ž $\frac{1}{2}${8i$\sqrt{3}$} = 4$\sqrt{3}$i

Hence (3) is correct answer.