Solve (24+10i)*(-65-72i)

$$( 24 + 10 i ) \times ( - 65 - 72 i )$$

Evaluate

$$-840-2378i$$

Solution Steps

Multiply complex numbers 24+10i and -65-72i like you multiply binomials.

$$24\left(-65\right)+24\times \left(-72i\right)+10i\left(-65\right)+10\left(-72\right)i^{2}$$

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

$$24\left(-65\right)+24\times \left(-72i\right)+10i\left(-65\right)+10\left(-72\right)\left(-1\right)$$

Do the multiplications.

$$-1560-1728i-650i+720$$

Combine the real and imaginary parts.

$$-1560+720+\left(-1728-650\right)i$$

Do the additions.

$$-840-2378i$$

Real Part

$$-840$$

Solution Steps

Multiply complex numbers 24+10i and -65-72i like you multiply binomials.

$$Re(24\left(-65\right)+24\times \left(-72i\right)+10i\left(-65\right)+10\left(-72\right)i^{2})$$

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

$$Re(24\left(-65\right)+24\times \left(-72i\right)+10i\left(-65\right)+10\left(-72\right)\left(-1\right))$$

Do the multiplications in 24\left(-65\right)+24\times \left(-72i\right)+10i\left(-65\right)+10\left(-72\right)\left(-1\right).

$$Re(-1560-1728i-650i+720)$$

Combine the real and imaginary parts in -1560-1728i-650i+720.

$$Re(-1560+720+\left(-1728-650\right)i)$$

Do the additions in -1560+720+\left(-1728-650\right)i.

$$Re(-840-2378i)$$

The real part of -840-2378i is -840.

$$-840$$