Solve 5i^2(9+i)(9-i)+sqrt{-144}+i^7

$$5 i ^ { 2 } ( 9 + i ) ( 9 - i ) + \sqrt { - 144 } + i ^ { 7 }$$

Evaluate

$$-410+11i$$

Solution Steps

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

$$5\left(-1\right)\left(9+i\right)\left(9-i\right)+\sqrt{-144}+i^{7}$$

Multiply 5 and -1 to get -5.

$$-5\left(9+i\right)\left(9-i\right)+\sqrt{-144}+i^{7}$$

Multiply -5 and 9+i to get -45-5i.

$$\left(-45-5i\right)\left(9-i\right)+\sqrt{-144}+i^{7}$$

Multiply -45-5i and 9-i to get -410.

$$-410+\sqrt{-144}+i^{7}$$

Calculate the square root of -144 and get 12i.

$$-410+12i+i^{7}$$

Calculate i to the power of 7 and get -i.

$$-410+12i-i$$

Do the additions.

$$-410+11i$$

Real Part

$$-410$$

Solution Steps

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

$$Re(5\left(-1\right)\left(9+i\right)\left(9-i\right)+\sqrt{-144}+i^{7})$$

Multiply 5 and -1 to get -5.

$$Re(-5\left(9+i\right)\left(9-i\right)+\sqrt{-144}+i^{7})$$

Multiply -5 and 9+i to get -45-5i.

$$Re(\left(-45-5i\right)\left(9-i\right)+\sqrt{-144}+i^{7})$$

Multiply -45-5i and 9-i to get -410.

$$Re(-410+\sqrt{-144}+i^{7})$$

Calculate the square root of -144 and get 12i.

$$Re(-410+12i+i^{7})$$

Calculate i to the power of 7 and get -i.

$$Re(-410+12i-i)$$

Do the additions in -410+12i-i.

$$Re(-410+11i)$$

The real part of -410+11i is -410.

$$-410$$