Solve (9-2i)(-4-6i)

$$( 9 - 2 i ) ( - 4 - 6 i )$$

Evaluate

$$-48-46i$$

Solution Steps

Multiply complex numbers 9-2i and -4-6i like you multiply binomials.

$$9\left(-4\right)+9\times \left(-6i\right)-2i\left(-4\right)-2\left(-6\right)i^{2}$$

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

$$9\left(-4\right)+9\times \left(-6i\right)-2i\left(-4\right)-2\left(-6\right)\left(-1\right)$$

Do the multiplications.

$$-36-54i+8i-12$$

Combine the real and imaginary parts.

$$-36-12+\left(-54+8\right)i$$

Do the additions.

$$-48-46i$$

Real Part

$$-48$$

Solution Steps

Multiply complex numbers 9-2i and -4-6i like you multiply binomials.

$$Re(9\left(-4\right)+9\times \left(-6i\right)-2i\left(-4\right)-2\left(-6\right)i^{2})$$

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

$$Re(9\left(-4\right)+9\times \left(-6i\right)-2i\left(-4\right)-2\left(-6\right)\left(-1\right))$$

Do the multiplications in 9\left(-4\right)+9\times \left(-6i\right)-2i\left(-4\right)-2\left(-6\right)\left(-1\right).

$$Re(-36-54i+8i-12)$$

Combine the real and imaginary parts in -36-54i+8i-12.

$$Re(-36-12+\left(-54+8\right)i)$$

Do the additions in -36-12+\left(-54+8\right)i.

$$Re(-48-46i)$$

The real part of -48-46i is -48.

$$-48$$