Solve z_{1}*z_{2}=(1-i)(sqrt{3}+i)

$$z _ { 1 } \cdot z _ { 2 } = ( 1 - i ) ( \sqrt { 3 } + i )$$

Solve for z_1

$$z_{1}=-\frac{\sqrt{3}\left(-1+i\right)+\left(-1-i\right)}{z_{2}}$$

$$z_{2}\neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply 1-i by \sqrt{3}+i.

$$z_{1}z_{2}=\left(1-i\right)\sqrt{3}+\left(1+i\right)$$

The equation is in standard form.

$$z_{2}z_{1}=\sqrt{3}\left(1-i\right)+\left(1+i\right)$$

Divide both sides by z_{2}.

$$\frac{z_{2}z_{1}}{z_{2}}=\frac{\sqrt{3}\left(1-i\right)+\left(1+i\right)}{z_{2}}$$

Dividing by z_{2} undoes the multiplication by z_{2}.

$$z_{1}=\frac{\sqrt{3}\left(1-i\right)+\left(1+i\right)}{z_{2}}$$

Solve for z_2

$$z_{2}=-\frac{\sqrt{3}\left(-1+i\right)+\left(-1-i\right)}{z_{1}}$$

$$z_{1}\neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply 1-i by \sqrt{3}+i.

$$z_{1}z_{2}=\left(1-i\right)\sqrt{3}+\left(1+i\right)$$

The equation is in standard form.

$$z_{1}z_{2}=\sqrt{3}\left(1-i\right)+\left(1+i\right)$$

Divide both sides by z_{1}.

$$\frac{z_{1}z_{2}}{z_{1}}=\frac{\sqrt{3}\left(1-i\right)+\left(1+i\right)}{z_{1}}$$

Dividing by z_{1} undoes the multiplication by z_{1}.

$$z_{2}=\frac{\sqrt{3}\left(1-i\right)+\left(1+i\right)}{z_{1}}$$