Solve 3i^3-sqrt{-4}+3sqrt{-9}-2+i^2

$$3 i ^ { 3 } - \sqrt { - 4 } + 3 \sqrt { - 9 } - 2 + i ^ { 2 }$$

Evaluate

$$-3+4i$$

Solution Steps

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

$$3\left(-i\right)-\sqrt{-4}+3\sqrt{-9}-2+i^{2}$$

Multiply 3 and -i to get -3i.

$$-3i-\sqrt{-4}+3\sqrt{-9}-2+i^{2}$$

Calculate the square root of -4 and get 2i.

$$-3i-2i+3\sqrt{-9}-2+i^{2}$$

Do the additions.

$$3\sqrt{-9}+i^{2}-2-5i$$

Calculate the square root of -9 and get 3i.

$$3\times \left(3i\right)+i^{2}-2-5i$$

Multiply 3 and 3i to get 9i.

$$9i+i^{2}-2-5i$$

Do the additions.

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

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

$$-1-2+4i$$

Do the additions.

$$-3+4i$$

Real Part

$$-3$$

Solution Steps

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

$$Re(3\left(-i\right)-\sqrt{-4}+3\sqrt{-9}-2+i^{2})$$

Multiply 3 and -i to get -3i.

$$Re(-3i-\sqrt{-4}+3\sqrt{-9}-2+i^{2})$$

Calculate the square root of -4 and get 2i.

$$Re(-3i-2i+3\sqrt{-9}-2+i^{2})$$

Do the additions in -3i-2i-2.

$$Re(3\sqrt{-9}+i^{2}-2-5i)$$

Calculate the square root of -9 and get 3i.

$$Re(3\times \left(3i\right)+i^{2}-2-5i)$$

Multiply 3 and 3i to get 9i.

$$Re(9i+i^{2}-2-5i)$$

Do the additions in 9i-2-5i.

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

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

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

Do the additions in -1-2+4i.

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

The real part of -3+4i is -3.

$$-3$$