Solve (1+i)x=2i

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

Solve for x

$$x=1+i$$

Steps for Solving Linear Equation

Divide both sides by 1+i.

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

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

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

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

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

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

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

Multiply 2i times 1-i.

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

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

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

Do the multiplications in 2i\times 1+2\left(-1\right)\left(-1\right). Reorder the terms.

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

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

$$x=1+i$$