Solve 3ileft(2+5iright)+2left(3-2iright)

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

Evaluate

$$-9+2i$$

Solution Steps

Multiply 3i times 2+5i.

$$3i\times 2+3\times 5i^{2}+2\left(3-2i\right)$$

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

$$3i\times 2+3\times 5\left(-1\right)+2\left(3-2i\right)$$

Do the multiplications in 3i\times 2+3\times 5\left(-1\right). Reorder the terms.

$$-15+6i+2\left(3-2i\right)$$

Multiply 2 times 3-2i.

$$-15+6i+2\times 3+2\times \left(-2i\right)$$

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

$$-15+6i+\left(6-4i\right)$$

Combine the real and imaginary parts.

$$-15+6+\left(6-4\right)i$$

Do the additions.

$$-9+2i$$

Real Part

$$-9$$

Solution Steps

Multiply 3i times 2+5i.

$$Re(3i\times 2+3\times 5i^{2}+2\left(3-2i\right))$$

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

$$Re(3i\times 2+3\times 5\left(-1\right)+2\left(3-2i\right))$$

Do the multiplications in 3i\times 2+3\times 5\left(-1\right). Reorder the terms.

$$Re(-15+6i+2\left(3-2i\right))$$

Multiply 2 times 3-2i.

$$Re(-15+6i+2\times 3+2\times \left(-2i\right))$$

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

$$Re(-15+6i+\left(6-4i\right))$$

Combine the real and imaginary parts in -15+6i+6-4i.

$$Re(-15+6+\left(6-4\right)i)$$

Do the additions in -15+6+\left(6-4\right)i.

$$Re(-9+2i)$$

The real part of -9+2i is -9.

$$-9$$