# Question 1, Exercise 1.2

Solutions of Question 1 of Exercise 1.2 of Unit 01: Complex Numbers. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan.

### Question 1(i)

Show that for any complex number, $\operatorname{Re}(i z)=-\operatorname{Im}(z)$.

**Solution.**
Suppose $$z=x+iy$$
\begin{align}
iz&=i(x+iy)\\
&=ix-y\end{align}
Now
\begin{align}Re(iz)&=-y\\
\implies Re(iz)&=-Im(z)\end{align}

### Question 1(ii)

Show that for any complex number, $\operatorname{Im}(i z)=\operatorname{Re}(z)$.

**Solution.**
Suppose $$z=x+iy$$
\begin{align}iz&=i(x+iy)\\
&=ix-y\end{align}
Now \begin{align}Im(iz)&=x\\
\implies Im(iz)&=Re(z)\end{align}

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