Solve 4i^80+3i^83-2i^-82

$$4 i ^ { 80 } + 3 i ^ { 83 } - 2 i ^ { - 82 }$$

Evaluate

$$6-3i$$

Solution Steps

Calculate i to the power of 80 and get 1.

$$4\times 1+3i^{83}-2i^{-82}$$

Multiply 4 and 1 to get 4.

$$4+3i^{83}-2i^{-82}$$

Calculate i to the power of 83 and get -i.

$$4+3\left(-i\right)-2i^{-82}$$

Multiply 3 and -i to get -3i.

$$4-3i-2i^{-82}$$

Calculate i to the power of -82 and get -1.

$$4-3i-2\left(-1\right)$$

Multiply 2 and -1 to get -2.

$$4-3i-\left(-2\right)$$

The opposite of -2 is 2.

$$4-3i+2$$

Add 4-3i and 2 to get 6-3i.

$$6-3i$$

Real Part

$$6$$

Solution Steps

Calculate i to the power of 80 and get 1.

$$Re(4\times 1+3i^{83}-2i^{-82})$$

Multiply 4 and 1 to get 4.

$$Re(4+3i^{83}-2i^{-82})$$

Calculate i to the power of 83 and get -i.

$$Re(4+3\left(-i\right)-2i^{-82})$$

Multiply 3 and -i to get -3i.

$$Re(4-3i-2i^{-82})$$

Calculate i to the power of -82 and get -1.

$$Re(4-3i-2\left(-1\right))$$

Multiply 2 and -1 to get -2.

$$Re(4-3i-\left(-2\right))$$

The opposite of -2 is 2.

$$Re(4-3i+2)$$

Add 4-3i and 2 to get 6-3i.

$$Re(6-3i)$$

The real part of 6-3i is 6.

$$6$$