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Question

If (z2)(z3)=2 represents a circle, then find its radius.

A
23
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B
43
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C
23
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D
43
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Solution

The correct option is A 23
z2z3=2
or |z2|2=4|z3|2
|x2+iy|2=4|x3+iy|2
or (x2)2+y2=4[(x3)2+y2]
or 3x2+3y224x+4x+364=0
or x2+y2203x+323=0
This represents a circle with center (103,0) and radius (1009)(323)=49=23

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