Solve 3i(2+2i)

$$3 i ( 2 + 2 i )$$

Evaluate

$$-6+6i$$

Solution Steps

Multiply 3i times 2+2i.

$$3i\times 2+3\times 2i^{2}$$

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

$$3i\times 2+3\times 2\left(-1\right)$$

Do the multiplications. Reorder the terms.

$$-6+6i$$

Real Part

$$-6$$

Solution Steps

Multiply 3i times 2+2i.

$$Re(3i\times 2+3\times 2i^{2})$$

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

$$Re(3i\times 2+3\times 2\left(-1\right))$$

Do the multiplications in 3i\times 2+3\times 2\left(-1\right). Reorder the terms.

$$Re(-6+6i)$$

The real part of -6+6i is -6.

$$-6$$