Solve 2+ai/1+i=3+i

$$\frac { 2 + a i } { 1 + i } = 3 + i$$

Solve for a

$$a=4$$

Steps for Solving Linear Equation

Multiply both sides by 1+i.

$$2+ai=\left(3+i\right)\left(1+i\right)$$

Multiply complex numbers 3+i and 1+i like you multiply binomials.

$$2+ai=3\times 1+3i+i+i^{2}$$

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

$$2+ai=3\times 1+3i+i-1$$

Do the multiplications in 3\times 1+3i+i-1.

$$2+ai=3+3i+i-1$$

Combine the real and imaginary parts in 3+3i+i-1.

$$2+ai=3-1+\left(3+1\right)i$$

Do the additions in 3-1+\left(3+1\right)i.

$$2+ai=2+4i$$

Subtract 2 from both sides.

$$ai=2+4i-2$$

Subtract 2 from 2+4i by subtracting corresponding real and imaginary parts.

$$ai=2-2+4i$$

Subtract 2 from 2 to get 0.

$$ai=4i$$

Divide both sides by i.

$$a=\frac{4i}{i}$$

Divide 4i by i to get 4.

$$a=4$$