Solve i^5=a+bi

$$i ^ { 5 } = a + b i$$

Solve for a

$$a=i-ib$$

Solution Steps

Calculate i to the power of 5 and get i.

$$i=a+bi$$

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

$$a+bi=i$$

Subtract bi from both sides.

$$a=i-bi$$

Multiply -1 and i to get -i.

$$a=i-ib$$

Solve for b

$$b=ia+1$$

Steps for Solving Linear Equation

Calculate i to the power of 5 and get i.

$$i=a+bi$$

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

$$a+bi=i$$

Subtract a from both sides.

$$bi=i-a$$

The equation is in standard form.

$$ib=i-a$$

Divide both sides by i.

$$\frac{ib}{i}=\frac{i-a}{i}$$

Dividing by i undoes the multiplication by i.

$$b=\frac{i-a}{i}$$

Divide i-a by i.

$$b=ia+1$$