(ii) z−zˉ2i=Im(z)\frac{z-\bar{z}}{2i}=\operatorname{Im}(z)2iz−zˉ=Im(z) Solution Let z=a+ib, a,b∈R.Then zˉ=a−ib.z−zˉ=(a+ib)−(a−ib)=2ibz−zˉ2i=2ib2i=b=Im(z)\begin{aligned} & \boxed{\text{Let } z=a+ib,\ a,b\in\mathbb{R}.} \\ \\ & \boxed{\text{Then } \bar{z}=a-ib.} \\ \\ & z-\bar{z}=(a+ib)-(a-ib)=2ib \\ \\ & \frac{z-\bar{z}}{2i}=\frac{2ib}{2i}=b=\operatorname{Im}(z) \end{aligned}Let z=a+ib, a,b∈R.Then zˉ=a−ib.z−zˉ=(a+ib)−(a−ib)=2ib2iz−zˉ=2i2ib=b=Im(z)