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

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Re⁡zz0=1

zz0+z0z=2r2

Im⁡zz0=1

Im⁡z0z=1

answer is A.

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Detailed Solution

∠OAP=π2⇒ z−z0z0 is purely imaginary⇒ z−z0z0+z−z0z0=0or zz0+zz0=2 (1)⇒ Re⁡zz0=1From (1),zz0+z0z=2z02=2r2

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