Solve 71/2+81/5-6i/4+21/10

$$7 \frac { 1 } { 2 } + 8 \frac { 1 } { 5 } - 6 \frac { i } { 4 } + 2 \frac { 1 } { 10 }$$

Evaluate

$$\frac{89}{5}-\frac{3}{2}i=17.8-1.5i$$

Solution Steps

Multiply 7 and 2 to get 14.

$$\frac{14+1}{2}+\frac{8\times 5+1}{5}-6\times \frac{i}{4}+\frac{2\times 10+1}{10}$$

Add 14 and 1 to get 15.

$$\frac{15}{2}+\frac{8\times 5+1}{5}-6\times \frac{i}{4}+\frac{2\times 10+1}{10}$$

Multiply 8 and 5 to get 40.

$$\frac{15}{2}+\frac{40+1}{5}-6\times \frac{i}{4}+\frac{2\times 10+1}{10}$$

Add 40 and 1 to get 41.

$$\frac{15}{2}+\frac{41}{5}-6\times \frac{i}{4}+\frac{2\times 10+1}{10}$$

Least common multiple of 2 and 5 is 10. Convert \frac{15}{2} and \frac{41}{5} to fractions with denominator 10.

$$\frac{75}{10}+\frac{82}{10}-6\times \frac{i}{4}+\frac{2\times 10+1}{10}$$

Since \frac{75}{10} and \frac{82}{10} have the same denominator, add them by adding their numerators.

$$\frac{75+82}{10}-6\times \frac{i}{4}+\frac{2\times 10+1}{10}$$

Add 75 and 82 to get 157.

$$\frac{157}{10}-6\times \frac{i}{4}+\frac{2\times 10+1}{10}$$

Divide i by 4 to get \frac{1}{4}i.

$$\frac{157}{10}-6\times \left(\frac{1}{4}i\right)+\frac{2\times 10+1}{10}$$

Multiply 6 and \frac{1}{4}i to get \frac{3}{2}i.

$$\frac{157}{10}-\frac{3}{2}i+\frac{2\times 10+1}{10}$$

Multiply 2 and 10 to get 20.

$$\frac{157}{10}-\frac{3}{2}i+\frac{20+1}{10}$$

Add 20 and 1 to get 21.

$$\frac{157}{10}-\frac{3}{2}i+\frac{21}{10}$$

Combine the real and imaginary parts in numbers \frac{157}{10}-\frac{3}{2}i and \frac{21}{10}.

$$\frac{157}{10}+\frac{21}{10}-\frac{3}{2}i$$

Add \frac{157}{10} to \frac{21}{10}.

$$\frac{89}{5}-\frac{3}{2}i$$

Real Part

$$\frac{89}{5} = 17\frac{4}{5} = 17.8$$

Solution Steps

Multiply 7 and 2 to get 14.

$$Re(\frac{14+1}{2}+\frac{8\times 5+1}{5}-6\times \frac{i}{4}+\frac{2\times 10+1}{10})$$

Add 14 and 1 to get 15.

$$Re(\frac{15}{2}+\frac{8\times 5+1}{5}-6\times \frac{i}{4}+\frac{2\times 10+1}{10})$$

Multiply 8 and 5 to get 40.

$$Re(\frac{15}{2}+\frac{40+1}{5}-6\times \frac{i}{4}+\frac{2\times 10+1}{10})$$

Add 40 and 1 to get 41.

$$Re(\frac{15}{2}+\frac{41}{5}-6\times \frac{i}{4}+\frac{2\times 10+1}{10})$$

Least common multiple of 2 and 5 is 10. Convert \frac{15}{2} and \frac{41}{5} to fractions with denominator 10.

$$Re(\frac{75}{10}+\frac{82}{10}-6\times \frac{i}{4}+\frac{2\times 10+1}{10})$$

Since \frac{75}{10} and \frac{82}{10} have the same denominator, add them by adding their numerators.

$$Re(\frac{75+82}{10}-6\times \frac{i}{4}+\frac{2\times 10+1}{10})$$

Add 75 and 82 to get 157.

$$Re(\frac{157}{10}-6\times \frac{i}{4}+\frac{2\times 10+1}{10})$$

Divide i by 4 to get \frac{1}{4}i.

$$Re(\frac{157}{10}-6\times \left(\frac{1}{4}i\right)+\frac{2\times 10+1}{10})$$

Multiply 6 and \frac{1}{4}i to get \frac{3}{2}i.

$$Re(\frac{157}{10}-\frac{3}{2}i+\frac{2\times 10+1}{10})$$

Multiply 2 and 10 to get 20.

$$Re(\frac{157}{10}-\frac{3}{2}i+\frac{20+1}{10})$$

Add 20 and 1 to get 21.

$$Re(\frac{157}{10}-\frac{3}{2}i+\frac{21}{10})$$

Combine the real and imaginary parts in numbers \frac{157}{10}-\frac{3}{2}i and \frac{21}{10}.

$$Re(\frac{157}{10}+\frac{21}{10}-\frac{3}{2}i)$$

Add \frac{157}{10} to \frac{21}{10}.

$$Re(\frac{89}{5}-\frac{3}{2}i)$$

The real part of \frac{89}{5}-\frac{3}{2}i is \frac{89}{5}.

$$\frac{89}{5}$$