Let z,w be complex number such that z¯+iw¯=0 and arg (zw)=π then Arg (z)=

Z¯=−iW¯⇒z=iW⇒ arg Z=argi+argw argZ−argw=π2−(1) & argt+arg w=π−(2) From (1)&(2) argz=3π4

Let z,w be complex number such that z¯+iw¯=0 and arg (zw)=π then Arg (z)=

Z¯=−iW¯⇒z=iW⇒ arg Z=argi+argw argZ−argw=π2−(1) & argt+arg w=π−(2) From (1)&(2) argz=3π4

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Let $z, w$ be complex number such that $\bar{z} + i \bar{w} = 0$ and arg $(z w) = π$ then Arg $(z) =$

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$\frac{π}{4}$

$\frac{5 π}{4}$

$\frac{π}{2}$

$\frac{3 π}{4}$

answer is D.

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Detailed Solution

$\bar{Z} = - i \bar{W} \Rightarrow z = i W \Rightarrow a r g Z = \arg i + \arg w \arg Z - \arg w = \frac{π}{2} - (1) & \arg t + \arg w = π - (2) F r o m (1) & (2) a r g z = \frac{3 π}{4}$

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Let z,w be complex number such that z¯+iw¯=0 and arg (zw)=π then Arg (z)=

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Let $z, w$ be complex number such that $\bar{z} + i \bar{w} = 0$ and arg $(z w) = π$ then Arg $(z) =$