Solve 4-i^6/2+i

$$\frac { 4 - i ^ { 6 } } { 2 + i }$$

Evaluate

$$2-i$$

Solution Steps

Calculate i to the power of 6 and get -1.

$$\frac{4-\left(-1\right)}{2+i}$$

The opposite of -1 is 1.

$$\frac{4+1}{2+i}$$

Add 4 and 1 to get 5.

$$\frac{5}{2+i}$$

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

$$\frac{5\left(2-i\right)}{\left(2+i\right)\left(2-i\right)}$$

Do the multiplications in \frac{5\left(2-i\right)}{\left(2+i\right)\left(2-i\right)}.

$$\frac{10-5i}{5}$$

Divide 10-5i by 5 to get 2-i.

$$2-i$$

Real Part

$$2$$

Solution Steps

Calculate i to the power of 6 and get -1.

$$Re(\frac{4-\left(-1\right)}{2+i})$$

The opposite of -1 is 1.

$$Re(\frac{4+1}{2+i})$$

Add 4 and 1 to get 5.

$$Re(\frac{5}{2+i})$$

Multiply both numerator and denominator of \frac{5}{2+i} by the complex conjugate of the denominator, 2-i.

$$Re(\frac{5\left(2-i\right)}{\left(2+i\right)\left(2-i\right)})$$

Do the multiplications in \frac{5\left(2-i\right)}{\left(2+i\right)\left(2-i\right)}.

$$Re(\frac{10-5i}{5})$$

Divide 10-5i by 5 to get 2-i.

$$Re(2-i)$$

The real part of 2-i is 2.

$$2$$