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

Straight line

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Circle

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Ellipse

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Parabola

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Solution

The correct option is B
Circle

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

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