Solve z=5/1-2i

$$z = \frac { 5 } { 1 - 2 i }$$

Solve for z

$$z=1+2i$$

Steps for Solving Linear Equation

Multiply both numerator and denominator of \frac{5}{1-2i} by the complex conjugate of the denominator, 1+2i.

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

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

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

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

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

Multiply 5 times 1+2i.

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

Do the multiplications in 5\times 1+5\times \left(2i\right).

$$z=\frac{5+10i}{5}$$

Divide 5+10i by 5 to get 1+2i.

$$z=1+2i$$

Assign z

$$z≔1+2i$$