Solve 24/1-i

$$\frac { 24 } { 1 - i }$$

Evaluate

$$12+12i$$

Solution Steps

Multiply both numerator and denominator by the complex conjugate of the denominator, 1+i.

$$\frac{24\left(1+i\right)}{\left(1-i\right)\left(1+i\right)}$$

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

$$\frac{24\left(1+i\right)}{1^{2}-i^{2}}$$

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

$$\frac{24\left(1+i\right)}{2}$$

Multiply 24 times 1+i.

$$\frac{24\times 1+24i}{2}$$

Do the multiplications in 24\times 1+24i.

$$\frac{24+24i}{2}$$

Divide 24+24i by 2 to get 12+12i.

$$12+12i$$

Real Part

$$12$$

Solution Steps

Multiply both numerator and denominator of \frac{24}{1-i} by the complex conjugate of the denominator, 1+i.

$$Re(\frac{24\left(1+i\right)}{\left(1-i\right)\left(1+i\right)})$$

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

$$Re(\frac{24\left(1+i\right)}{1^{2}-i^{2}})$$

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

$$Re(\frac{24\left(1+i\right)}{2})$$

Multiply 24 times 1+i.

$$Re(\frac{24\times 1+24i}{2})$$

Do the multiplications in 24\times 1+24i.

$$Re(\frac{24+24i}{2})$$

Divide 24+24i by 2 to get 12+12i.

$$Re(12+12i)$$

The real part of 12+12i is 12.

$$12$$