Statement-I: If z=z¯ then z is purely imaginaryStatement-II: If z=-z¯ then z is purely real

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Statement-I: If z= $\bar{z}$ then z is purely imaginary

Statement-II: If z=- $\bar{z}$ then z is purely real

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Both I and II are true

Neither I nor II are true

Only I is true

Only II is true

answer is D.

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Detailed Solution

$Let z = x + iy \Rightarrow z = x - iy z = z \Rightarrow x + iy = x - iy \Rightarrow 2 iy = 0 \Rightarrow y = 0 \Rightarrow z = x is purely real$

$z = - z \Rightarrow x + iy = - (x - iy) \Rightarrow x + iy = - x + iy \Rightarrow 2 x = 0 \Rightarrow x = 0 \Rightarrow z = iy is purely imaginary$

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