Solve (1+1)((3+i)(5-1)/2-1)/2-1=

$$\frac { ( 1 + 1 ) ( \frac { ( 3 + i ) ( 5 - 1 ) } { 2 } - 1 ) } { 2 } - 1 =$$

Evaluate

$$4+2i$$

Solution Steps

Add 1 and 1 to get 2.

$$\frac{2\left(\frac{\left(3+i\right)\left(5-1\right)}{2}-1\right)}{2}-1$$

Subtract 1 from 5 to get 4.

$$\frac{2\left(\frac{\left(3+i\right)\times 4}{2}-1\right)}{2}-1$$

Multiply 3+i times 4.

$$\frac{2\left(\frac{3\times 4+4i}{2}-1\right)}{2}-1$$

Do the multiplications in 3\times 4+4i.

$$\frac{2\left(\frac{12+4i}{2}-1\right)}{2}-1$$

Divide 12+4i by 2 to get 6+2i.

$$\frac{2\left(6+2i-1\right)}{2}-1$$

Subtract 1 from 6+2i by subtracting corresponding real and imaginary parts.

$$\frac{2\left(6-1+2i\right)}{2}-1$$

Subtract 1 from 6 to get 5.

$$\frac{2\left(5+2i\right)}{2}-1$$

Multiply 2 times 5+2i.

$$\frac{2\times 5+2\times \left(2i\right)}{2}-1$$

Do the multiplications in 2\times 5+2\times \left(2i\right).

$$\frac{10+4i}{2}-1$$

Divide 10+4i by 2 to get 5+2i.

$$5+2i-1$$

Subtract 1 from 5+2i by subtracting corresponding real and imaginary parts.

$$5-1+2i$$

Subtract 1 from 5 to get 4.

$$4+2i$$

Real Part

$$4$$

Solution Steps

Add 1 and 1 to get 2.

$$Re(\frac{2\left(\frac{\left(3+i\right)\left(5-1\right)}{2}-1\right)}{2}-1)$$

Subtract 1 from 5 to get 4.

$$Re(\frac{2\left(\frac{\left(3+i\right)\times 4}{2}-1\right)}{2}-1)$$

Multiply 3+i times 4.

$$Re(\frac{2\left(\frac{3\times 4+4i}{2}-1\right)}{2}-1)$$

Do the multiplications in 3\times 4+4i.

$$Re(\frac{2\left(\frac{12+4i}{2}-1\right)}{2}-1)$$

Divide 12+4i by 2 to get 6+2i.

$$Re(\frac{2\left(6+2i-1\right)}{2}-1)$$

Subtract 1 from 6+2i by subtracting corresponding real and imaginary parts.

$$Re(\frac{2\left(6-1+2i\right)}{2}-1)$$

Subtract 1 from 6 to get 5.

$$Re(\frac{2\left(5+2i\right)}{2}-1)$$

Multiply 2 times 5+2i.

$$Re(\frac{2\times 5+2\times \left(2i\right)}{2}-1)$$

Do the multiplications in 2\times 5+2\times \left(2i\right).

$$Re(\frac{10+4i}{2}-1)$$

Divide 10+4i by 2 to get 5+2i.

$$Re(5+2i-1)$$

Subtract 1 from 5+2i by subtracting corresponding real and imaginary parts.

$$Re(5-1+2i)$$

Subtract 1 from 5 to get 4.

$$Re(4+2i)$$

The real part of 4+2i is 4.

$$4$$