Solve (1+2i)2i

$$( 1 + 2 i ) 2 i$$

Evaluate

$$-4+2i$$

Solution Steps

Multiply 1+2i times 2i.

$$1\times \left(2i\right)+2\times 2i^{2}$$

By definition, i^{2} is -1.

$$1\times \left(2i\right)+2\times 2\left(-1\right)$$

Do the multiplications. Reorder the terms.

$$-4+2i$$

Real Part

$$-4$$

Solution Steps

Multiply 1+2i times 2i.

$$Re(1\times \left(2i\right)+2\times 2i^{2})$$

By definition, i^{2} is -1.

$$Re(1\times \left(2i\right)+2\times 2\left(-1\right))$$

Do the multiplications in 1\times \left(2i\right)+2\times 2\left(-1\right). Reorder the terms.

$$Re(-4+2i)$$

The real part of -4+2i is -4.

$$-4$$