Solve -1/2i^3(sqrt{-9}-4)-3i^2

$$- \frac { 1 } { 2 } i ^ { 3 } ( \sqrt { - 9 } - 4 ) - 3 i ^ { 2 }$$

Evaluate

$$\frac{3}{2}-2i=1.5-2i$$

Solution Steps

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

$$-\frac{1}{2}\left(-i\right)\left(\sqrt{-9}-4\right)-3i^{2}$$

Multiply -\frac{1}{2} and -i to get \frac{1}{2}i.

$$\frac{1}{2}i\left(\sqrt{-9}-4\right)-3i^{2}$$

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

$$\frac{1}{2}i\left(3i-4\right)-3i^{2}$$

Use the distributive property to multiply \frac{1}{2}i by 3i-4.

$$-\frac{3}{2}-2i-3i^{2}$$

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

$$-\frac{3}{2}-2i-3\left(-1\right)$$

Multiply 3 and -1 to get -3.

$$-\frac{3}{2}-2i-\left(-3\right)$$

The opposite of -3 is 3.

$$-\frac{3}{2}-2i+3$$

Add -\frac{3}{2}-2i and 3 to get \frac{3}{2}-2i.

$$\frac{3}{2}-2i$$

Real Part

$$\frac{3}{2} = 1\frac{1}{2} = 1.5$$

Solution Steps

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

$$Re(-\frac{1}{2}\left(-i\right)\left(\sqrt{-9}-4\right)-3i^{2})$$

Multiply -\frac{1}{2} and -i to get \frac{1}{2}i.

$$Re(\frac{1}{2}i\left(\sqrt{-9}-4\right)-3i^{2})$$

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

$$Re(\frac{1}{2}i\left(3i-4\right)-3i^{2})$$

Use the distributive property to multiply \frac{1}{2}i by 3i-4.

$$Re(-\frac{3}{2}-2i-3i^{2})$$

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

$$Re(-\frac{3}{2}-2i-3\left(-1\right))$$

Multiply 3 and -1 to get -3.

$$Re(-\frac{3}{2}-2i-\left(-3\right))$$

The opposite of -3 is 3.

$$Re(-\frac{3}{2}-2i+3)$$

Add -\frac{3}{2}-2i and 3 to get \frac{3}{2}-2i.

$$Re(\frac{3}{2}-2i)$$

The real part of \frac{3}{2}-2i is \frac{3}{2}.

$$\frac{3}{2}$$