Solve (-2-i)x=5

$$( - 2 - i ) x = 5$$

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}.

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

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

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

Multiply 5 times -2+i.

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

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

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

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

$$x=-2+i$$