Solve 3/6i^21-2+(3/2i^3-1/4)-i^18=

$$\frac { 3 } { 6 } i ^ { 21 } - 2 + ( \frac { 3 } { 2 } i ^ { 3 } - \frac { 1 } { 4 } ) - i ^ { 18 } =$$

Evaluate

$$-\frac{5}{4}-i=-1.25-i$$

Solution Steps

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

$$\frac{1}{2}i^{21}-2+\frac{3}{2}i^{3}-\frac{1}{4}-i^{18}$$

Calculate i to the power of 21 and get i.

$$\frac{1}{2}i-2+\frac{3}{2}i^{3}-\frac{1}{4}-i^{18}$$

Do the additions in \frac{1}{2}i-2-\frac{1}{4}.

$$\frac{3}{2}i^{3}-\frac{9}{4}+\frac{1}{2}i-i^{18}$$

Calculate i to the power of 18 and get -1.

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

The opposite of -1 is 1.

$$\frac{3}{2}i^{3}-\frac{9}{4}+\frac{1}{2}i+1$$

Do the additions.

$$\frac{3}{2}i^{3}-\frac{5}{4}+\frac{1}{2}i$$

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

$$\frac{3}{2}\left(-i\right)-\frac{5}{4}+\frac{1}{2}i$$

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

$$-\frac{3}{2}i-\frac{5}{4}+\frac{1}{2}i$$

Do the additions.

$$-\frac{5}{4}-i$$

Real Part

$$-\frac{5}{4} = -1\frac{1}{4} = -1.25$$

Solution Steps

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

$$Re(\frac{1}{2}i^{21}-2+\frac{3}{2}i^{3}-\frac{1}{4}-i^{18})$$

Calculate i to the power of 21 and get i.

$$Re(\frac{1}{2}i-2+\frac{3}{2}i^{3}-\frac{1}{4}-i^{18})$$

Do the additions in \frac{1}{2}i-2-\frac{1}{4}.

$$Re(\frac{3}{2}i^{3}-\frac{9}{4}+\frac{1}{2}i-i^{18})$$

Calculate i to the power of 18 and get -1.

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

The opposite of -1 is 1.

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

Do the additions in -\frac{9}{4}+\frac{1}{2}i+1.

$$Re(\frac{3}{2}i^{3}-\frac{5}{4}+\frac{1}{2}i)$$

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

$$Re(\frac{3}{2}\left(-i\right)-\frac{5}{4}+\frac{1}{2}i)$$

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

$$Re(-\frac{3}{2}i-\frac{5}{4}+\frac{1}{2}i)$$

Do the additions in -\frac{3}{2}i-\frac{5}{4}+\frac{1}{2}i.

$$Re(-\frac{5}{4}-i)$$

The real part of -\frac{5}{4}-i is -\frac{5}{4}.

$$-\frac{5}{4}$$