Solve 2+26/-3-3i=

$$\frac { 2 + 26 } { - 3 - 3 i } =$$

Evaluate

$$-\frac{14}{3}+\frac{14}{3}i\approx -4.666666667+4.666666667i$$

Solution Steps

Add 2 and 26 to get 28.

$$\frac{28}{-3-3i}$$

Multiply both numerator and denominator by the complex conjugate of the denominator, -3+3i.

$$\frac{28\left(-3+3i\right)}{\left(-3-3i\right)\left(-3+3i\right)}$$

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

$$\frac{28\left(-3+3i\right)}{\left(-3\right)^{2}-3^{2}i^{2}}$$

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

$$\frac{28\left(-3+3i\right)}{18}$$

Multiply 28 times -3+3i.

$$\frac{28\left(-3\right)+28\times \left(3i\right)}{18}$$

Do the multiplications in 28\left(-3\right)+28\times \left(3i\right).

$$\frac{-84+84i}{18}$$

Divide -84+84i by 18 to get -\frac{14}{3}+\frac{14}{3}i.

$$-\frac{14}{3}+\frac{14}{3}i$$

Real Part

$$-\frac{14}{3} = -4\frac{2}{3} = -4.666666666666667$$

Solution Steps

Add 2 and 26 to get 28.

$$Re(\frac{28}{-3-3i})$$

Multiply both numerator and denominator of \frac{28}{-3-3i} by the complex conjugate of the denominator, -3+3i.

$$Re(\frac{28\left(-3+3i\right)}{\left(-3-3i\right)\left(-3+3i\right)})$$

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

$$Re(\frac{28\left(-3+3i\right)}{\left(-3\right)^{2}-3^{2}i^{2}})$$

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

$$Re(\frac{28\left(-3+3i\right)}{18})$$

Multiply 28 times -3+3i.

$$Re(\frac{28\left(-3\right)+28\times \left(3i\right)}{18})$$

Do the multiplications in 28\left(-3\right)+28\times \left(3i\right).

$$Re(\frac{-84+84i}{18})$$

Divide -84+84i by 18 to get -\frac{14}{3}+\frac{14}{3}i.

$$Re(-\frac{14}{3}+\frac{14}{3}i)$$

The real part of -\frac{14}{3}+\frac{14}{3}i is -\frac{14}{3}.

$$-\frac{14}{3}$$