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Question

Let z1 satisfy the condition |z3|=2 and z2 satisfy the equation |z1|+|z+1|=3. If |z1z2|min=m and |z1z2|max=M, then which of the following is/are correct?

A
M+m=92
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B
M2+m2+Mm=814
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C
M2+m2+Mm=1694
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D
M+m=132
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Solution

The correct options are
C M2+m2+Mm=1694
D M+m=132
|z1|+|z+1|=3

Ellipse: Centre (0,0), 2a=3, 2ae=2

|z3|=2 Circle with centre (3,0),r=2



m=|z1z2|min=0 as curves intersect.

|z1z2|max=5+32=132=M

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