Solve i^4-2i^2+1/i^3-i^5

$$\frac { i ^ { 4 } - 2 i ^ { 2 } + 1 } { i ^ { 3 } - i ^ { 5 } }$$

Evaluate

$$2i$$

Solution Steps

Calculate i to the power of 4 and get 1.

$$\frac{1-2i^{2}+1}{i^{3}-i^{5}}$$

Calculate i to the power of 2 and get -1.

$$\frac{1-2\left(-1\right)+1}{i^{3}-i^{5}}$$

Multiply 2 and -1 to get -2.

$$\frac{1-\left(-2\right)+1}{i^{3}-i^{5}}$$

The opposite of -2 is 2.

$$\frac{1+2+1}{i^{3}-i^{5}}$$

Add 1 and 2 to get 3.

$$\frac{3+1}{i^{3}-i^{5}}$$

Add 3 and 1 to get 4.

$$\frac{4}{i^{3}-i^{5}}$$

Calculate i to the power of 3 and get -i.

$$\frac{4}{-i-i^{5}}$$

Calculate i to the power of 5 and get i.

$$\frac{4}{-i-i}$$

Subtract i from -i to get -2i.

$$\frac{4}{-2i}$$

Multiply both numerator and denominator by imaginary unit i.

$$\frac{4i}{2}$$

Divide 4i by 2 to get 2i.

$$2i$$

Real Part

$$0$$

Solution Steps

Calculate i to the power of 4 and get 1.

$$Re(\frac{1-2i^{2}+1}{i^{3}-i^{5}})$$

Calculate i to the power of 2 and get -1.

$$Re(\frac{1-2\left(-1\right)+1}{i^{3}-i^{5}})$$

Multiply 2 and -1 to get -2.

$$Re(\frac{1-\left(-2\right)+1}{i^{3}-i^{5}})$$

The opposite of -2 is 2.

$$Re(\frac{1+2+1}{i^{3}-i^{5}})$$

Add 1 and 2 to get 3.

$$Re(\frac{3+1}{i^{3}-i^{5}})$$

Add 3 and 1 to get 4.

$$Re(\frac{4}{i^{3}-i^{5}})$$

Calculate i to the power of 3 and get -i.

$$Re(\frac{4}{-i-i^{5}})$$

Calculate i to the power of 5 and get i.

$$Re(\frac{4}{-i-i})$$

Subtract i from -i to get -2i.

$$Re(\frac{4}{-2i})$$

Multiply both numerator and denominator of \frac{4}{-2i} by imaginary unit i.

$$Re(\frac{4i}{2})$$

Divide 4i by 2 to get 2i.

$$Re(2i)$$

The real part of 2i is 0.

$$0$$