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Question

If ω=zz-13i and |ω|=1, then z lies on


A

A parabola

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B

A straight line

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C

A circle

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D

An ellipse

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Solution

The correct option is B

A straight line


Explanation for the correct option.

Step 1: Assumption and simplification required for the solution.

Let the complex number zbex+iy.

As given that ω=1 and ω=zz-13i

Now take mod on both sides of the equation ω=zz-13i

ω=zz-13i

This gives

1=zz-13i

Step 2: Calculation for the correct option

Since z=x+iy then

1=x+iyx+iy-13i

Solving the above equation,

x+iy-13i=x+iy3x+3iy-i=3x+3iy3x+3y-1i=3x2+3iy23x2+3y-12=9x2+y29x2+1+9y2-6y=9x2+9y26y-1=0

This is an equation of a straight line.

Hence, the correct option is (B).


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