Solveeit Logo
Login

Question

Question: If 27iZ<sup>3</sup> + 18Z<sup>2</sup> –12Z + 8i = 0, then...

If 27iZ3 + 18Z2 –12Z + 8i = 0, then

A

|Z| = 32\frac{3}{2}

B

|Z| = 1

C

|Z| = 43\frac{4}{3}

D

|Z| = 23\frac{2}{3}

Answer

|Z| = 23\frac{2}{3}

Explanation

Solution

Sol. 27iZ3 + 18Z2 –12Z + 8i = 0

Ž 9iZ2 (3Z –2i) –4 (3Z –2i) = 0

Ž (3Z –2i) (9iZ2 –4) = 0

Ž Z =23\frac{2}{3}i or Z2 = –49\frac{4}{9}i

In either case, |Z| = 23\frac{2}{3}