Solve (frac{sqrt{3}}{2}+1/2)+(frac{sqrt{3}}{2}-1/2)+(12/2+i)+(1/2-i)=

$$( \frac { \sqrt { 3 } } { 2 } + \frac { 1 } { 2 } ) + ( \frac { \sqrt { 3 } } { 2 } - \frac { 1 } { 2 } ) + ( \frac { 12 } { 2 } + i ) + ( \frac { 1 } { 2 } - i ) =$$

Evaluate

$$\sqrt{3}+\frac{13}{2}\approx 8.232050808$$

Solution Steps

Combine the real and imaginary parts.

$$\frac{\sqrt{3}}{2}+\frac{\sqrt{3}}{2}+\frac{12}{2}+\frac{1}{2}-\frac{1}{2}+\frac{1}{2}+\left(1-1\right)i$$

Do the additions.

$$\frac{\sqrt{3}}{2}+\frac{\sqrt{3}}{2}+\frac{12}{2}+\frac{1}{2}$$

Combine \frac{\sqrt{3}}{2} and \frac{\sqrt{3}}{2} to get \sqrt{3}.

$$\sqrt{3}+\frac{12}{2}+\frac{1}{2}$$

Since \frac{12}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$\sqrt{3}+\frac{12+1}{2}$$

Add 12 and 1 to get 13.

$$\sqrt{3}+\frac{13}{2}$$

Real Part

$$\sqrt{3} + \frac{13}{2} = 8.232050808$$