1) if z and w are complex numbers such that ¯z−i¯w=0 and Arg (zw) = 3π4, then Arg z= A) π16 B) π8 C) π4 D) 3π4 Answer: Option BExplanation: We have, ¯z−i¯w=0 ⇒ i¯w=¯z⇒w=1i¯z ⇒ w=−1iz⇒w=iz Now , we have arg(zw)= 3π4 ⇒ arg(z(iz))= 3π4 ⇒ arg(iz2)= 3π4 ⇒ arg(i)+arg(z2)= 3π4 [∵arg(z1z2)=arg(z1)+arg(z2)] ⇒ arg(i)+2arg(z)=3π4 [ ∵arg(zn)=narg(z)] ⇒ π2+2arg(z)=3π4 ⇒ arg(z)= π8