Solve 21/left(1-iright)^3

$$\frac{ 21 }{ { \left(1-i \right) }^{ 3 } }$$

Evaluate

$$-\frac{21}{4}+\frac{21}{4}i=-5.25+5.25i$$

Solution Steps

Calculate 1-i to the power of 3 and get -2-2i.

$$\frac{21}{-2-2i}$$

Multiply both numerator and denominator by the complex conjugate of the denominator, -2+2i.

$$\frac{21\left(-2+2i\right)}{\left(-2-2i\right)\left(-2+2i\right)}$$

Do the multiplications in \frac{21\left(-2+2i\right)}{\left(-2-2i\right)\left(-2+2i\right)}.

$$\frac{-42+42i}{8}$$

Divide -42+42i by 8 to get -\frac{21}{4}+\frac{21}{4}i.

$$-\frac{21}{4}+\frac{21}{4}i$$

Real Part

$$-\frac{21}{4} = -5\frac{1}{4} = -5.25$$

Solution Steps

Calculate 1-i to the power of 3 and get -2-2i.

$$Re(\frac{21}{-2-2i})$$

Multiply both numerator and denominator of \frac{21}{-2-2i} by the complex conjugate of the denominator, -2+2i.

$$Re(\frac{21\left(-2+2i\right)}{\left(-2-2i\right)\left(-2+2i\right)})$$

Do the multiplications in \frac{21\left(-2+2i\right)}{\left(-2-2i\right)\left(-2+2i\right)}.

$$Re(\frac{-42+42i}{8})$$

Divide -42+42i by 8 to get -\frac{21}{4}+\frac{21}{4}i.

$$Re(-\frac{21}{4}+\frac{21}{4}i)$$

The real part of -\frac{21}{4}+\frac{21}{4}i is -\frac{21}{4}.

$$-\frac{21}{4}$$