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

$$2 i ^ { 3 } + 3 i ^ { 2 } - 5 i ^ { 4 }$$

Evaluate

$$-8-2i$$

Solution Steps

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

$$2\left(-i\right)+3i^{2}-5i^{4}$$

Multiply 2 and -i to get -2i.

$$-2i+3i^{2}-5i^{4}$$

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

$$-2i+3\left(-1\right)-5i^{4}$$

Multiply 3 and -1 to get -3.

$$-2i-3-5i^{4}$$

Calculate i to the power of 4 and get 1.

$$-2i-3-5\times 1$$

Multiply 5 and 1 to get 5.

$$-2i-3-5$$

Do the additions.

$$-8-2i$$

Real Part

$$-8$$

Solution Steps

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

$$Re(2\left(-i\right)+3i^{2}-5i^{4})$$

Multiply 2 and -i to get -2i.

$$Re(-2i+3i^{2}-5i^{4})$$

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

$$Re(-2i+3\left(-1\right)-5i^{4})$$

Multiply 3 and -1 to get -3.

$$Re(-2i-3-5i^{4})$$

Calculate i to the power of 4 and get 1.

$$Re(-2i-3-5\times 1)$$

Multiply 5 and 1 to get 5.

$$Re(-2i-3-5)$$

Do the additions in -2i-3-5.

$$Re(-8-2i)$$

The real part of -8-2i is -8.

$$-8$$