Solve -3+2i(2-4i+6+5i-3-2i)

$$- 3 + 2 i ( 2 - 4 i + 6 + 5 i - 3 - 2 i )$$

Evaluate

$$-1+10i$$

Solution Steps

Combine the real and imaginary parts in 2-4i+6+5i-3-2i.

$$-3+2i\left(2+6-3+\left(-4+5-2\right)i\right)$$

Do the additions in 2+6-3+\left(-4+5-2\right)i.

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

Multiply 2i times 5-i.

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

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

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

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

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

Combine the real and imaginary parts.

$$-3+2+10i$$

Add -3 to 2.

$$-1+10i$$

Real Part

$$-1$$

Solution Steps

Combine the real and imaginary parts in 2-4i+6+5i-3-2i.

$$Re(-3+2i\left(2+6-3+\left(-4+5-2\right)i\right))$$

Do the additions in 2+6-3+\left(-4+5-2\right)i.

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

Multiply 2i times 5-i.

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

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

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

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

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

Combine the real and imaginary parts in -3+2+10i.

$$Re(-3+2+10i)$$

Add -3 to 2.

$$Re(-1+10i)$$

The real part of -1+10i is -1.

$$-1$$