Solve 1/2(0.2)(1.25)+i/2(0.2)(1.25)=

$$\frac { 1 } { 2 } ( 0.2 ) ( 1.25 ) + \frac { i } { 2 } ( 0.2 ) ( 1.25 ) =$$

Evaluate

$$0.125+0.125i$$

Solution Steps

Convert decimal number 0.2 to fraction \frac{2}{10}. Reduce the fraction \frac{2}{10} to lowest terms by extracting and canceling out 2.

$$\frac{1}{2}\times \frac{1}{5}\times 1.25+\frac{i}{2}\times 0.2\times 1.25$$

Multiply \frac{1}{2} times \frac{1}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 1}{2\times 5}\times 1.25+\frac{i}{2}\times 0.2\times 1.25$$

Do the multiplications in the fraction \frac{1\times 1}{2\times 5}.

$$\frac{1}{10}\times 1.25+\frac{i}{2}\times 0.2\times 1.25$$

Convert decimal number 1.25 to fraction \frac{125}{100}. Reduce the fraction \frac{125}{100} to lowest terms by extracting and canceling out 25.

$$\frac{1}{10}\times \frac{5}{4}+\frac{i}{2}\times 0.2\times 1.25$$

Multiply \frac{1}{10} times \frac{5}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 5}{10\times 4}+\frac{i}{2}\times 0.2\times 1.25$$

Do the multiplications in the fraction \frac{1\times 5}{10\times 4}.

$$\frac{5}{40}+\frac{i}{2}\times 0.2\times 1.25$$

Reduce the fraction \frac{5}{40} to lowest terms by extracting and canceling out 5.

$$\frac{1}{8}+\frac{i}{2}\times 0.2\times 1.25$$

Divide i by 2 to get \frac{1}{2}i.

$$\frac{1}{8}+\frac{1}{2}i\times 0.2\times 1.25$$

Multiply \frac{1}{2}i and 0.2 to get \frac{1}{10}i.

$$\frac{1}{8}+\frac{1}{10}i\times 1.25$$

Multiply \frac{1}{10}i and 1.25 to get \frac{1}{8}i.

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

Real Part

$$0.125$$

Solution Steps

Convert decimal number 0.2 to fraction \frac{2}{10}. Reduce the fraction \frac{2}{10} to lowest terms by extracting and canceling out 2.

$$Re(\frac{1}{2}\times \frac{1}{5}\times 1.25+\frac{i}{2}\times 0.2\times 1.25)$$

Multiply \frac{1}{2} times \frac{1}{5} by multiplying numerator times numerator and denominator times denominator.

$$Re(\frac{1\times 1}{2\times 5}\times 1.25+\frac{i}{2}\times 0.2\times 1.25)$$

Do the multiplications in the fraction \frac{1\times 1}{2\times 5}.

$$Re(\frac{1}{10}\times 1.25+\frac{i}{2}\times 0.2\times 1.25)$$

Convert decimal number 1.25 to fraction \frac{125}{100}. Reduce the fraction \frac{125}{100} to lowest terms by extracting and canceling out 25.

$$Re(\frac{1}{10}\times \frac{5}{4}+\frac{i}{2}\times 0.2\times 1.25)$$

Multiply \frac{1}{10} times \frac{5}{4} by multiplying numerator times numerator and denominator times denominator.

$$Re(\frac{1\times 5}{10\times 4}+\frac{i}{2}\times 0.2\times 1.25)$$

Do the multiplications in the fraction \frac{1\times 5}{10\times 4}.

$$Re(\frac{5}{40}+\frac{i}{2}\times 0.2\times 1.25)$$

Reduce the fraction \frac{5}{40} to lowest terms by extracting and canceling out 5.

$$Re(\frac{1}{8}+\frac{i}{2}\times 0.2\times 1.25)$$

Divide i by 2 to get \frac{1}{2}i.

$$Re(\frac{1}{8}+\frac{1}{2}i\times 0.2\times 1.25)$$

Multiply \frac{1}{2}i and 0.2 to get \frac{1}{10}i.

$$Re(\frac{1}{8}+\frac{1}{10}i\times 1.25)$$

Multiply \frac{1}{10}i and 1.25 to get \frac{1}{8}i.

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

The real part of \frac{1}{8}+\frac{1}{8}i is \frac{1}{8}.

$$\frac{1}{8}$$