Solve -4i^9-2i^79-5i^112+8i^45

$$- 4 i ^ { 9 } - 2 i ^ { 79 } - 5 i ^ { 112 } + 8 i ^ { 45 }$$

Evaluate

$$-5+6i$$

Solution Steps

Calculate i to the power of 9 and get i.

$$-4i-2i^{79}-5i^{112}+8i^{45}$$

Calculate i to the power of 79 and get -i.

$$-4i-2\left(-i\right)-5i^{112}+8i^{45}$$

Multiply 2 and -i to get -2i.

$$-4i-\left(-2i\right)-5i^{112}+8i^{45}$$

The opposite of -2i is 2i.

$$-4i+2i-5i^{112}+8i^{45}$$

Add -4i and 2i to get -2i.

$$-2i-5i^{112}+8i^{45}$$

Calculate i to the power of 112 and get 1.

$$-2i-5\times 1+8i^{45}$$

Multiply 5 and 1 to get 5.

$$-2i-5+8i^{45}$$

Calculate i to the power of 45 and get i.

$$-2i-5+8i$$

Do the additions.

$$-5+6i$$

Real Part

$$-5$$

Solution Steps

Calculate i to the power of 9 and get i.

$$Re(-4i-2i^{79}-5i^{112}+8i^{45})$$

Calculate i to the power of 79 and get -i.

$$Re(-4i-2\left(-i\right)-5i^{112}+8i^{45})$$

Multiply 2 and -i to get -2i.

$$Re(-4i-\left(-2i\right)-5i^{112}+8i^{45})$$

The opposite of -2i is 2i.

$$Re(-4i+2i-5i^{112}+8i^{45})$$

Add -4i and 2i to get -2i.

$$Re(-2i-5i^{112}+8i^{45})$$

Calculate i to the power of 112 and get 1.

$$Re(-2i-5\times 1+8i^{45})$$

Multiply 5 and 1 to get 5.

$$Re(-2i-5+8i^{45})$$

Calculate i to the power of 45 and get i.

$$Re(-2i-5+8i)$$

Do the additions in -2i-5+8i.

$$Re(-5+6i)$$

The real part of -5+6i is -5.

$$-5$$