Solve -4/7-6i

$$- \frac { 4 } { 7 - 6 i }$$

Evaluate

$$-\frac{28}{85}-\frac{24}{85}i\approx -0.329411765-0.282352941i$$

Solution Steps

Multiply both numerator and denominator of \frac{4}{7-6i} by the complex conjugate of the denominator, 7+6i.

$$-\frac{4\left(7+6i\right)}{\left(7-6i\right)\left(7+6i\right)}$$

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$-\frac{4\left(7+6i\right)}{7^{2}-6^{2}i^{2}}$$

By definition, i^{2} is -1. Calculate the denominator.

$$-\frac{4\left(7+6i\right)}{85}$$

Multiply 4 times 7+6i.

$$-\frac{4\times 7+4\times \left(6i\right)}{85}$$

Do the multiplications in 4\times 7+4\times \left(6i\right).

$$-\frac{28+24i}{85}$$

Divide 28+24i by 85 to get \frac{28}{85}+\frac{24}{85}i.

$$-\frac{28}{85}-\frac{24}{85}i$$

Real Part

$$-\frac{28}{85} = -0.32941176470588235$$

Solution Steps

Multiply both numerator and denominator of \frac{4}{7-6i} by the complex conjugate of the denominator, 7+6i.

$$Re(-\frac{4\left(7+6i\right)}{\left(7-6i\right)\left(7+6i\right)})$$

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$Re(-\frac{4\left(7+6i\right)}{7^{2}-6^{2}i^{2}})$$

By definition, i^{2} is -1. Calculate the denominator.

$$Re(-\frac{4\left(7+6i\right)}{85})$$

Multiply 4 times 7+6i.

$$Re(-\frac{4\times 7+4\times \left(6i\right)}{85})$$

Do the multiplications in 4\times 7+4\times \left(6i\right).

$$Re(-\frac{28+24i}{85})$$

Divide 28+24i by 85 to get \frac{28}{85}+\frac{24}{85}i.

$$Re(-\frac{28}{85}-\frac{24}{85}i)$$

The real part of -\frac{28}{85}-\frac{24}{85}i is -\frac{28}{85}.

$$-\frac{28}{85}$$