Question

All the roots of the equation 11z¹⁰ + 10iz⁹ +10iz – 11 = 0 lie

• A. Inside |z| = 1
• B. On |z| = 1
• C. Outside |z| = 1
• D. Can't say

Answer 1

Answer: (B)

On |z| = 1

Answer 2

Sol. z⁹ (11z + 10i) = 11 –10iz

Ž z⁹ = $\frac{11 - 10iz}{11z + 10i}$

Ž |z⁹| = $\frac{|11i - 10z|}{|11z + 10i|}$

Ž |11i + 10z|² –|11z + 10i|2 = 21 (1 –|z|²)

Ž if |z| < 1, then |z⁹| > 1 (not possible) and if |z| > 1 Ž |z⁹| < 1 (not possible)

Ž |z| = 1