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

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

Evaluate

$$18-46i$$

Solution Steps

Multiply complex numbers -6+2i and -5+6i like you multiply binomials.

$$-6\left(-5\right)-6\times \left(6i\right)+2i\left(-5\right)+2\times 6i^{2}$$

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

$$-6\left(-5\right)-6\times \left(6i\right)+2i\left(-5\right)+2\times 6\left(-1\right)$$

Do the multiplications.

$$30-36i-10i-12$$

Combine the real and imaginary parts.

$$30-12+\left(-36-10\right)i$$

Do the additions.

$$18-46i$$

Real Part

$$18$$

Solution Steps

Multiply complex numbers -6+2i and -5+6i like you multiply binomials.

$$Re(-6\left(-5\right)-6\times \left(6i\right)+2i\left(-5\right)+2\times 6i^{2})$$

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

$$Re(-6\left(-5\right)-6\times \left(6i\right)+2i\left(-5\right)+2\times 6\left(-1\right))$$

Do the multiplications in -6\left(-5\right)-6\times \left(6i\right)+2i\left(-5\right)+2\times 6\left(-1\right).

$$Re(30-36i-10i-12)$$

Combine the real and imaginary parts in 30-36i-10i-12.

$$Re(30-12+\left(-36-10\right)i)$$

Do the additions in 30-12+\left(-36-10\right)i.

$$Re(18-46i)$$

The real part of 18-46i is 18.

$$18$$