Question

The solutions of the equation z⁴ + 4z³i – 6z² – 4zi – i = 0 are the vertices of a convex polygon in the complex plane. The area of the polygon is :

• A. 2^3/4
• B. 2^3/2
• C. 2^5/4
• D. 2

Answer 1

Answer: (C)

2^5/4

Answer 2

Sol. z⁴+ 4z³i + 6z²i² + 4zi³ + i⁴ = 1 + i

Ž (z + i)⁴ = 1 + i Ž |z + i| = $\left( \sqrt{2} \right)^{1/4}$

Area = 4.$\frac{1}{2}$ |z + i|² = 2(2)^1/4 = 2^5/4