Solve 7i^17-6i^6+3i^3-2i^2+1

$$7 i ^ { 17 } - 6 i ^ { 6 } + 3 i ^ { 3 } - 2 i ^ { 2 } + 1$$

Evaluate

$$9+4i$$

Solution Steps

Calculate i to the power of 17 and get i.

$$7i-6i^{6}+3i^{3}-2i^{2}+1$$

Calculate i to the power of 6 and get -1.

$$7i-6\left(-1\right)+3i^{3}-2i^{2}+1$$

Multiply 6 and -1 to get -6.

$$7i-\left(-6\right)+3i^{3}-2i^{2}+1$$

The opposite of -6 is 6.

$$7i+6+3i^{3}-2i^{2}+1$$

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

$$7i+6+3\left(-i\right)-2i^{2}+1$$

Multiply 3 and -i to get -3i.

$$7i+6-3i-2i^{2}+1$$

Do the additions in 7i+6-3i.

$$6+4i-2i^{2}+1$$

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

$$6+4i-2\left(-1\right)+1$$

Multiply 2 and -1 to get -2.

$$6+4i-\left(-2\right)+1$$

The opposite of -2 is 2.

$$6+4i+2+1$$

Add 6+4i and 2 to get 8+4i.

$$8+4i+1$$

Add 8+4i and 1 to get 9+4i.

$$9+4i$$

Real Part

$$9$$

Solution Steps

Calculate i to the power of 17 and get i.

$$Re(7i-6i^{6}+3i^{3}-2i^{2}+1)$$

Calculate i to the power of 6 and get -1.

$$Re(7i-6\left(-1\right)+3i^{3}-2i^{2}+1)$$

Multiply 6 and -1 to get -6.

$$Re(7i-\left(-6\right)+3i^{3}-2i^{2}+1)$$

The opposite of -6 is 6.

$$Re(7i+6+3i^{3}-2i^{2}+1)$$

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

$$Re(7i+6+3\left(-i\right)-2i^{2}+1)$$

Multiply 3 and -i to get -3i.

$$Re(7i+6-3i-2i^{2}+1)$$

Do the additions in 7i+6-3i.

$$Re(6+4i-2i^{2}+1)$$

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

$$Re(6+4i-2\left(-1\right)+1)$$

Multiply 2 and -1 to get -2.

$$Re(6+4i-\left(-2\right)+1)$$

The opposite of -2 is 2.

$$Re(6+4i+2+1)$$

Add 6+4i and 2 to get 8+4i.

$$Re(8+4i+1)$$

Add 8+4i and 1 to get 9+4i.

$$Re(9+4i)$$

The real part of 9+4i is 9.

$$9$$