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Question

Equation of tangent drawn to circle |z|=r at the point A(z0) is

A
Re(zz0)=1
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B
z¯¯¯z0z0¯¯¯z=2r2
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C
Im(zz0)=1
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D
z¯¯¯z0+z0¯¯¯z=2r2
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Solution

The correct option is D z¯¯¯z0+z0¯¯¯z=2r2
OAP=π2
zz0z0 is purely imaginary
zz0z0+¯¯¯z¯¯¯z0¯¯¯z0=0
zz0+¯¯¯z¯¯¯z0=2(1)
Re(zz0)=1

From (1),
z¯z0+z0¯z=2|z0|2=2r2

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