Solve z=3-1/1+2i

$$z = \frac { 3 - 1 } { 1 + 2 i }$$

Solve for z

$$z=\frac{2}{5}-\frac{4}{5}i=0.4-0.8i$$

Steps for Solving Linear Equation

Subtract 1 from 3 to get 2.

$$z=\frac{2}{1+2i}$$

Multiply both numerator and denominator of \frac{2}{1+2i} by the complex conjugate of the denominator, 1-2i.

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

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

By definition, i^{2} is -1. Calculate the denominator.

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

Multiply 2 times 1-2i.

$$z=\frac{2\times 1+2\times \left(-2i\right)}{5}$$

Do the multiplications in 2\times 1+2\times \left(-2i\right).

$$z=\frac{2-4i}{5}$$

Divide 2-4i by 5 to get \frac{2}{5}-\frac{4}{5}i.

$$z=\frac{2}{5}-\frac{4}{5}i$$

Assign z

$$z≔\frac{2}{5}-\frac{4}{5}i$$