Solve 2left(12+2i/4+iright)

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

Evaluate

$$6+3i$$

Solution Steps

Divide 12+2i by 4 to get 3+\frac{1}{2}i.

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

Combine the real and imaginary parts in numbers 3+\frac{1}{2}i and i.

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

Add \frac{1}{2} to 1.

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

Multiply 2 times 3+\frac{3}{2}i.

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

Do the multiplications.

$$6+3i$$

Real Part

$$6$$

Solution Steps

Divide 12+2i by 4 to get 3+\frac{1}{2}i.

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

Combine the real and imaginary parts in numbers 3+\frac{1}{2}i and i.

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

Add \frac{1}{2} to 1.

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

Multiply 2 times 3+\frac{3}{2}i.

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

Do the multiplications in 2\times 3+2\times \left(\frac{3}{2}i\right).

$$Re(6+3i)$$

The real part of 6+3i is 6.

$$6$$