Solve operatorname{Re}(iz)=-operatorname{Im}z:quad(b

$$\operatorname { Re } ( i z ) = - \operatorname { Im } z : \quad ( b$$

Solve for b

$$\left\{\begin{matrix}\\b=1\text{, }&\text{unconditionally}\\b\neq 0\text{, }&Im(z)=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable b cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by b.

$$bRe(iz)=-Im(z)$$

The equation is in standard form.

$$\left(-Im(z)\right)b=-Im(z)$$

Divide both sides by -Im(z).

$$\frac{\left(-Im(z)\right)b}{-Im(z)}=-\frac{Im(z)}{-Im(z)}$$

Dividing by -Im(z) undoes the multiplication by -Im(z).

$$b=-\frac{Im(z)}{-Im(z)}$$

Divide -Im(z) by -Im(z).

$$b=1$$