Solve (4+5i)*(2i)

$$( 4 + 5 i ) \times ( 2 i )$$

Evaluate

$$-10+8i$$

Solution Steps

Multiply 4+5i times 2i.

$$4\times \left(2i\right)+5\times 2i^{2}$$

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

$$4\times \left(2i\right)+5\times 2\left(-1\right)$$

Do the multiplications. Reorder the terms.

$$-10+8i$$

Real Part

$$-10$$

Solution Steps

Multiply 4+5i times 2i.

$$Re(4\times \left(2i\right)+5\times 2i^{2})$$

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

$$Re(4\times \left(2i\right)+5\times 2\left(-1\right))$$

Do the multiplications in 4\times \left(2i\right)+5\times 2\left(-1\right). Reorder the terms.

$$Re(-10+8i)$$

The real part of -10+8i is -10.

$$-10$$