Solve (i+1)^n=ai+b

$$( i + 1 ) ^ { n } = a i + b$$

Solve for a

$$a=ib-i\left(1+i\right)^{n}$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$ai+b=\left(i+1\right)^{n}$$

Subtract b from both sides.

$$ai=\left(i+1\right)^{n}-b$$

The equation is in standard form.

$$ia=\left(1+i\right)^{n}-b$$

Divide both sides by i.

$$\frac{ia}{i}=\frac{\left(1+i\right)^{n}-b}{i}$$

Dividing by i undoes the multiplication by i.

$$a=\frac{\left(1+i\right)^{n}-b}{i}$$

Divide \left(1+i\right)^{n}-b by i.

$$a=ib-i\left(1+i\right)^{n}$$

Solve for b

$$b=\left(1+i\right)^{n}-ia$$