Solve 5(4+i)^2/i(2+2)

$$\frac { 5 ( 4 + i ) ^ { 2 } } { i ( 2 + 2 ) }$$

Evaluate

$$10-\frac{75}{4}i=10-18.75i$$

Solution Steps

Calculate 4+i to the power of 2 and get 15+8i.

$$\frac{5\left(15+8i\right)}{i\left(2+2\right)}$$

Multiply 5 and 15+8i to get 75+40i.

$$\frac{75+40i}{i\left(2+2\right)}$$

Add 2 and 2 to get 4.

$$\frac{75+40i}{4i}$$

Multiply both numerator and denominator by imaginary unit i.

$$\frac{-40+75i}{-4}$$

Divide -40+75i by -4 to get 10-\frac{75}{4}i.

$$10-\frac{75}{4}i$$

Real Part

$$10$$

Solution Steps

Calculate 4+i to the power of 2 and get 15+8i.

$$Re(\frac{5\left(15+8i\right)}{i\left(2+2\right)})$$

Multiply 5 and 15+8i to get 75+40i.

$$Re(\frac{75+40i}{i\left(2+2\right)})$$

Add 2 and 2 to get 4.

$$Re(\frac{75+40i}{4i})$$

Multiply both numerator and denominator of \frac{75+40i}{4i} by imaginary unit i.

$$Re(\frac{-40+75i}{-4})$$

Divide -40+75i by -4 to get 10-\frac{75}{4}i.

$$Re(10-\frac{75}{4}i)$$

The real part of 10-\frac{75}{4}i is 10.

$$10$$