Solve (2-texttt{i})x=5

$$(2- \texttt{i} )x=5$$

Solve for x

$$x=2+i$$

Steps for Solving Linear Equation

Divide both sides by 2-i.

$$x=\frac{5}{2-i}$$

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

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

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

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

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

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

Multiply 5 times 2+i.

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

Do the multiplications in 5\times 2+5i.

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

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

$$x=2+i$$