Solve i^102+2i^6-7i^9+2^0

$$i ^ { 102 } + 2 i ^ { 6 } - 7 i ^ { 9 } + 2 ^ { 0 }$$

Evaluate

$$-2-7i$$

Solution Steps

Calculate i to the power of 102 and get -1.

$$-1+2i^{6}-7i^{9}+2^{0}$$

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

$$-1+2\left(-1\right)-7i^{9}+2^{0}$$

Multiply 2 and -1 to get -2.

$$-1-2-7i^{9}+2^{0}$$

Subtract 2 from -1 to get -3.

$$-3-7i^{9}+2^{0}$$

Calculate i to the power of 9 and get i.

$$-3-7i+2^{0}$$

Calculate 2 to the power of 0 and get 1.

$$-3-7i+1$$

Add -3-7i and 1 to get -2-7i.

$$-2-7i$$

Real Part

$$-2$$

Solution Steps

Calculate i to the power of 102 and get -1.

$$Re(-1+2i^{6}-7i^{9}+2^{0})$$

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

$$Re(-1+2\left(-1\right)-7i^{9}+2^{0})$$

Multiply 2 and -1 to get -2.

$$Re(-1-2-7i^{9}+2^{0})$$

Subtract 2 from -1 to get -3.

$$Re(-3-7i^{9}+2^{0})$$

Calculate i to the power of 9 and get i.

$$Re(-3-7i+2^{0})$$

Calculate 2 to the power of 0 and get 1.

$$Re(-3-7i+1)$$

Add -3-7i and 1 to get -2-7i.

$$Re(-2-7i)$$

The real part of -2-7i is -2.

$$-2$$