Solve -5(4)+(-5)(2i)+(3i)(4)+(3i)(2i)

$$- 5 ( 4 ) + ( - 5 ) ( 2 i ) + ( 3 i ) ( 4 ) + ( 3 i ) ( 2 i )$$

Evaluate

$$-26+2i$$

Solution Steps

Multiply -5 and 4 to get -20.

$$-20-5\times \left(2i\right)+3i\times 4+3i\times \left(2i\right)$$

Multiply -5 and 2i to get -10i.

$$-20-10i+3i\times 4+3i\times \left(2i\right)$$

Multiply 3i and 4 to get 12i.

$$-20-10i+12i+3i\times \left(2i\right)$$

Combine the real and imaginary parts.

$$3i\times \left(2i\right)-20+\left(-10+12\right)i$$

Add -10 to 12.

$$3i\times \left(2i\right)-20+2i$$

Combine 3i\times \left(2i\right) and 2i to get \left(1+3i\right)\times \left(2i\right).

$$\left(1+3i\right)\times \left(2i\right)-20$$

Multiply 1+3i times 2i.

$$1\times \left(2i\right)+3\times 2i^{2}-20$$

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

$$1\times \left(2i\right)+3\times 2\left(-1\right)-20$$

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

$$-6+2i-20$$

Combine the real and imaginary parts.

$$-6-20+2i$$

Add -6 to -20.

$$-26+2i$$

Real Part

$$-26$$

Solution Steps

Multiply -5 and 4 to get -20.

$$Re(-20-5\times \left(2i\right)+3i\times 4+3i\times \left(2i\right))$$

Multiply -5 and 2i to get -10i.

$$Re(-20-10i+3i\times 4+3i\times \left(2i\right))$$

Multiply 3i and 4 to get 12i.

$$Re(-20-10i+12i+3i\times \left(2i\right))$$

Combine the real and imaginary parts in -20-10i+12i.

$$Re(3i\times \left(2i\right)-20+\left(-10+12\right)i)$$

Add -10 to 12.

$$Re(3i\times \left(2i\right)-20+2i)$$

Combine 3i\times \left(2i\right) and 2i to get \left(1+3i\right)\times \left(2i\right).

$$Re(\left(1+3i\right)\times \left(2i\right)-20)$$

Multiply 1+3i times 2i.

$$Re(1\times \left(2i\right)+3\times 2i^{2}-20)$$

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

$$Re(1\times \left(2i\right)+3\times 2\left(-1\right)-20)$$

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

$$Re(-6+2i-20)$$

Combine the real and imaginary parts in -6+2i-20.

$$Re(-6-20+2i)$$

Add -6 to -20.

$$Re(-26+2i)$$

The real part of -26+2i is -26.

$$-26$$