Solve (1-2i)x=1

$$( 1 - 2 i ) x = 1$$

Solve for x

$$x=\frac{1}{5}+\frac{2}{5}i=0.2+0.4i$$

Steps for Solving Linear Equation

Divide both sides by 1-2i.

$$x=\frac{1}{1-2i}$$

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

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

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

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

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

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

Multiply 1 and 1+2i to get 1+2i.

$$x=\frac{1+2i}{5}$$

Divide 1+2i by 5 to get \frac{1}{5}+\frac{2}{5}i.

$$x=\frac{1}{5}+\frac{2}{5}i$$