Solve 2x=3/2+i

$$2 x = \frac { 3 } { 2 + i }$$

Solve for x

$$x=\frac{3}{5}-\frac{3}{10}i=0.6-0.3i$$

Steps for Solving Linear Equation

Multiply both numerator and denominator of \frac{3}{2+i} by the complex conjugate of the denominator, 2-i.

$$2x=\frac{3\left(2-i\right)}{\left(2+i\right)\left(2-i\right)}$$

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

$$2x=\frac{3\left(2-i\right)}{2^{2}-i^{2}}$$

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

$$2x=\frac{3\left(2-i\right)}{5}$$

Multiply 3 times 2-i.

$$2x=\frac{3\times 2+3\left(-i\right)}{5}$$

Do the multiplications in 3\times 2+3\left(-i\right).

$$2x=\frac{6-3i}{5}$$

Divide 6-3i by 5 to get \frac{6}{5}-\frac{3}{5}i.

$$2x=\frac{6}{5}-\frac{3}{5}i$$

Divide both sides by 2.

$$x=\frac{\frac{6}{5}-\frac{3}{5}i}{2}$$

Divide \frac{6}{5}-\frac{3}{5}i by 2 to get \frac{3}{5}-\frac{3}{10}i.

$$x=\frac{3}{5}-\frac{3}{10}i$$