Solve -5-4/-4-6i

$$\frac { - 5 - 4 } { - 4 - 6 i }$$

Evaluate

$$\frac{9}{13}-\frac{27}{26}i\approx 0.692307692-1.038461538i$$

Solution Steps

Subtract 4 from -5 to get -9.

$$\frac{-9}{-4-6i}$$

Multiply both numerator and denominator by the complex conjugate of the denominator, -4+6i.

$$\frac{-9\left(-4+6i\right)}{\left(-4-6i\right)\left(-4+6i\right)}$$

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

$$\frac{-9\left(-4+6i\right)}{\left(-4\right)^{2}-6^{2}i^{2}}$$

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

$$\frac{-9\left(-4+6i\right)}{52}$$

Multiply -9 times -4+6i.

$$\frac{-9\left(-4\right)-9\times \left(6i\right)}{52}$$

Do the multiplications in -9\left(-4\right)-9\times \left(6i\right).

$$\frac{36-54i}{52}$$

Divide 36-54i by 52 to get \frac{9}{13}-\frac{27}{26}i.

$$\frac{9}{13}-\frac{27}{26}i$$

Real Part

$$\frac{9}{13} = 0.6923076923076923$$

Solution Steps

Subtract 4 from -5 to get -9.

$$Re(\frac{-9}{-4-6i})$$

Multiply both numerator and denominator of \frac{-9}{-4-6i} by the complex conjugate of the denominator, -4+6i.

$$Re(\frac{-9\left(-4+6i\right)}{\left(-4-6i\right)\left(-4+6i\right)})$$

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

$$Re(\frac{-9\left(-4+6i\right)}{\left(-4\right)^{2}-6^{2}i^{2}})$$

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

$$Re(\frac{-9\left(-4+6i\right)}{52})$$

Multiply -9 times -4+6i.

$$Re(\frac{-9\left(-4\right)-9\times \left(6i\right)}{52})$$

Do the multiplications in -9\left(-4\right)-9\times \left(6i\right).

$$Re(\frac{36-54i}{52})$$

Divide 36-54i by 52 to get \frac{9}{13}-\frac{27}{26}i.

$$Re(\frac{9}{13}-\frac{27}{26}i)$$

The real part of \frac{9}{13}-\frac{27}{26}i is \frac{9}{13}.

$$\frac{9}{13}$$