Question

If $|$z$|$ = 3, then the points representing the complex numbers $-2+4z$ lie on a

• A. Straight line
• B. Circle
• C. Ellipse
• D. Parabola

Answer 1

The correct option is B

Circle

Let the complex number -2 + 4z be $\omega$
$\omega$ = -2 + 4z
$\omega$ + 2 = 4z
$|$$\omega$ + 2$|$ = 4$\left|z\right|$
$|$$\omega$ + 2$|$ = 12
This means the distance of all such w from (-2) is equal to 12. Such w lies on a circle
$\Rightarrow$$\omega$ represents a circle with centre -2 and radius 12.