Solve 1+i/2+frac{3{4}}

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

Evaluate

$$\frac{4}{11}+\frac{4}{11}i\approx 0.363636364+0.363636364i$$

Solution Steps

Convert 2 to fraction \frac{8}{4}.

$$\frac{1+i}{\frac{8}{4}+\frac{3}{4}}$$

Since \frac{8}{4} and \frac{3}{4} have the same denominator, add them by adding their numerators.

$$\frac{1+i}{\frac{8+3}{4}}$$

Add 8 and 3 to get 11.

$$\frac{1+i}{\frac{11}{4}}$$

Divide 1+i by \frac{11}{4} by multiplying 1+i by the reciprocal of \frac{11}{4}.

$$\left(1+i\right)\times \frac{4}{11}$$

Multiply 1+i times \frac{4}{11}.

$$1\times \frac{4}{11}+\frac{4}{11}i$$

Do the multiplications in 1\times \frac{4}{11}+\frac{4}{11}i.

$$\frac{4}{11}+\frac{4}{11}i$$

Real Part

$$\frac{4}{11} = 0.36363636363636365$$

Solution Steps

Convert 2 to fraction \frac{8}{4}.

$$Re(\frac{1+i}{\frac{8}{4}+\frac{3}{4}})$$

Since \frac{8}{4} and \frac{3}{4} have the same denominator, add them by adding their numerators.

$$Re(\frac{1+i}{\frac{8+3}{4}})$$

Add 8 and 3 to get 11.

$$Re(\frac{1+i}{\frac{11}{4}})$$

Divide 1+i by \frac{11}{4} by multiplying 1+i by the reciprocal of \frac{11}{4}.

$$Re(\left(1+i\right)\times \frac{4}{11})$$

Multiply 1+i times \frac{4}{11}.

$$Re(1\times \frac{4}{11}+\frac{4}{11}i)$$

Do the multiplications in 1\times \frac{4}{11}+\frac{4}{11}i.

$$Re(\frac{4}{11}+\frac{4}{11}i)$$

The real part of \frac{4}{11}+\frac{4}{11}i is \frac{4}{11}.

$$\frac{4}{11}$$