Solve z=-1-3i/sqrt{(-1)^2+(-2)^2}

$$z = \frac { - 1 - 3 i } { \sqrt { ( - 1 ) ^ { 2 } + ( - 2 ) ^ { 2 } } }$$

Solve for z

$$z=\sqrt{5}\left(-\frac{1}{5}-\frac{3}{5}i\right)\approx -0.447213595-1.341640786i$$

Steps for Solving Linear Equation

Calculate -1 to the power of 2 and get 1.

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

Calculate -2 to the power of 2 and get 4.

$$z=\frac{-1-3i}{\sqrt{1+4}}$$

Add 1 and 4 to get 5.

$$z=\frac{-1-3i}{\sqrt{5}}$$

Rationalize the denominator of \frac{-1-3i}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$z=\frac{\left(-1-3i\right)\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$z=\frac{\left(-1-3i\right)\sqrt{5}}{5}$$

Divide \left(-1-3i\right)\sqrt{5} by 5 to get \left(-\frac{1}{5}-\frac{3}{5}i\right)\sqrt{5}.

$$z=\left(-\frac{1}{5}-\frac{3}{5}i\right)\sqrt{5}$$

Assign z

$$z≔\sqrt{5}\left(-\frac{1}{5}-\frac{3}{5}i\right)$$