Solve (11/23-i22/46*5/7)-5/7

$$( \frac { 11 } { 23 } - i \frac { 22 } { 46 } \times \frac { 5 } { 7 } ) - \frac { 5 } { 7 }$$

Evaluate

$$-\frac{38}{161}-\frac{55}{161}i\approx -0.236024845-0.341614907i$$

Solution Steps

Reduce the fraction \frac{22}{46} to lowest terms by extracting and canceling out 2.

$$\frac{11}{23}-\frac{11}{23}i\times \frac{5}{7}-\frac{5}{7}$$

Multiply \frac{11}{23}i and \frac{5}{7} to get \frac{55}{161}i.

$$\frac{11}{23}-\frac{55}{161}i-\frac{5}{7}$$

Subtract \frac{5}{7} from \frac{11}{23}-\frac{55}{161}i by subtracting corresponding real and imaginary parts.

$$\frac{11}{23}-\frac{5}{7}-\frac{55}{161}i$$

Subtract \frac{5}{7} from \frac{11}{23} to get -\frac{38}{161}.

$$-\frac{38}{161}-\frac{55}{161}i$$

Real Part

$$-\frac{38}{161} = -0.2360248447204969$$

Solution Steps

Reduce the fraction \frac{22}{46} to lowest terms by extracting and canceling out 2.

$$Re(\frac{11}{23}-\frac{11}{23}i\times \frac{5}{7}-\frac{5}{7})$$

Multiply \frac{11}{23}i and \frac{5}{7} to get \frac{55}{161}i.

$$Re(\frac{11}{23}-\frac{55}{161}i-\frac{5}{7})$$

Subtract \frac{5}{7} from \frac{11}{23}-\frac{55}{161}i by subtracting corresponding real and imaginary parts.

$$Re(\frac{11}{23}-\frac{5}{7}-\frac{55}{161}i)$$

Subtract \frac{5}{7} from \frac{11}{23} to get -\frac{38}{161}.

$$Re(-\frac{38}{161}-\frac{55}{161}i)$$

The real part of -\frac{38}{161}-\frac{55}{161}i is -\frac{38}{161}.

$$-\frac{38}{161}$$