Question

If 8iz³ + 12z² – 18z + 27i = 0 , then-

• A. |z| = $\frac{3}{2}$
• B. |z| = $\frac{2}{3}$q
• C. |z| = 1
• D. |z| = $\frac{3}{4}$

Answer 1

Answer: (A)

|z| = $\frac{3}{2}$

Answer 2

Sol. We have 8iz³ + 12z² – 18z + 27i = 0

Ž 4z² (2iz + 3) + 9i (2iz + 3) = 0

Ž (2 iz + 3) (4z² + 9i) = 0

Ž 2iz + 3 = 0 or 4z² + 9i = 0

Ž z = – $\frac{3}{2i}$ or z² = –$\frac{9}{4}$i Ž |z| = $\left| - \frac{3}{2i} \right|$=$\frac{3}{2}$

or |z²| = $\left| - \frac{9}{4}i \right|$ = $\frac{9}{4}$ Ž |z|² = $\frac{9}{4}$ Ž |z| = $\frac{3}{2}$.