Solve 13i^4(2-i)/3-i

$$\frac { 13 i ^ { 4 } ( 2 - i ) } { 3 - i }$$

Evaluate

$$\frac{91}{10}-\frac{13}{10}i=9.1-1.3i$$

Solution Steps

Calculate i to the power of 4 and get 1.

$$\frac{13\times 1\left(2-i\right)}{3-i}$$

Multiply 13 and 1 to get 13.

$$\frac{13\left(2-i\right)}{3-i}$$

Multiply 13 and 2-i to get 26-13i.

$$\frac{26-13i}{3-i}$$

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

$$\frac{\left(26-13i\right)\left(3+i\right)}{\left(3-i\right)\left(3+i\right)}$$

Do the multiplications in \frac{\left(26-13i\right)\left(3+i\right)}{\left(3-i\right)\left(3+i\right)}.

$$\frac{91-13i}{10}$$

Divide 91-13i by 10 to get \frac{91}{10}-\frac{13}{10}i.

$$\frac{91}{10}-\frac{13}{10}i$$

Real Part

$$\frac{91}{10} = 9\frac{1}{10} = 9.1$$

Solution Steps

Calculate i to the power of 4 and get 1.

$$Re(\frac{13\times 1\left(2-i\right)}{3-i})$$

Multiply 13 and 1 to get 13.

$$Re(\frac{13\left(2-i\right)}{3-i})$$

Multiply 13 and 2-i to get 26-13i.

$$Re(\frac{26-13i}{3-i})$$

Multiply both numerator and denominator of \frac{26-13i}{3-i} by the complex conjugate of the denominator, 3+i.

$$Re(\frac{\left(26-13i\right)\left(3+i\right)}{\left(3-i\right)\left(3+i\right)})$$

Do the multiplications in \frac{\left(26-13i\right)\left(3+i\right)}{\left(3-i\right)\left(3+i\right)}.

$$Re(\frac{91-13i}{10})$$

Divide 91-13i by 10 to get \frac{91}{10}-\frac{13}{10}i.

$$Re(\frac{91}{10}-\frac{13}{10}i)$$

The real part of \frac{91}{10}-\frac{13}{10}i is \frac{91}{10}.

$$\frac{91}{10}$$