Solve 3(7-5i)(-3+4i)

$$3 ( 7 - 5 i ) ( - 3 + 4 i )$$

Evaluate

$$-3+129i$$

Solution Steps

Multiply 3 times 7-5i.

$$\left(3\times 7+3\times \left(-5i\right)\right)\left(-3+4i\right)$$

Do the multiplications.

$$\left(21-15i\right)\left(-3+4i\right)$$

Multiply complex numbers 21-15i and -3+4i like you multiply binomials.

$$21\left(-3\right)+21\times \left(4i\right)-15i\left(-3\right)-15\times 4i^{2}$$

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

$$21\left(-3\right)+21\times \left(4i\right)-15i\left(-3\right)-15\times 4\left(-1\right)$$

Do the multiplications.

$$-63+84i+45i+60$$

Combine the real and imaginary parts.

$$-63+60+\left(84+45\right)i$$

Do the additions.

$$-3+129i$$

Real Part

$$-3$$

Solution Steps

Multiply 3 times 7-5i.

$$Re(\left(3\times 7+3\times \left(-5i\right)\right)\left(-3+4i\right))$$

Do the multiplications in 3\times 7+3\times \left(-5i\right).

$$Re(\left(21-15i\right)\left(-3+4i\right))$$

Multiply complex numbers 21-15i and -3+4i like you multiply binomials.

$$Re(21\left(-3\right)+21\times \left(4i\right)-15i\left(-3\right)-15\times 4i^{2})$$

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

$$Re(21\left(-3\right)+21\times \left(4i\right)-15i\left(-3\right)-15\times 4\left(-1\right))$$

Do the multiplications in 21\left(-3\right)+21\times \left(4i\right)-15i\left(-3\right)-15\times 4\left(-1\right).

$$Re(-63+84i+45i+60)$$

Combine the real and imaginary parts in -63+84i+45i+60.

$$Re(-63+60+\left(84+45\right)i)$$

Do the additions in -63+60+\left(84+45\right)i.

$$Re(-3+129i)$$

The real part of -3+129i is -3.

$$-3$$