Solve 7(3-5i)+(4-2i)(-6+7i)

$$7 ( 3 - 5 i ) + ( 4 - 2 i ) ( - 6 + 7 i )$$

Evaluate

$$11+5i$$

Solution Steps

Multiply 7 times 3-5i.

$$7\times 3+7\times \left(-5i\right)+\left(4-2i\right)\left(-6+7i\right)$$

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

$$21-35i+\left(4-2i\right)\left(-6+7i\right)$$

Multiply complex numbers 4-2i and -6+7i like you multiply binomials.

$$21-35i+4\left(-6\right)+4\times \left(7i\right)-2i\left(-6\right)-2\times 7i^{2}$$

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

$$21-35i+4\left(-6\right)+4\times \left(7i\right)-2i\left(-6\right)-2\times 7\left(-1\right)$$

Do the multiplications in 4\left(-6\right)+4\times \left(7i\right)-2i\left(-6\right)-2\times 7\left(-1\right).

$$21-35i-24+28i+12i+14$$

Combine the real and imaginary parts in -24+28i+12i+14.

$$21-35i-24+14+\left(28+12\right)i$$

Do the additions in -24+14+\left(28+12\right)i.

$$21-35i+\left(-10+40i\right)$$

Combine the real and imaginary parts.

$$21-10+\left(-35+40\right)i$$

Do the additions.

$$11+5i$$

Real Part

$$11$$

Solution Steps

Multiply 7 times 3-5i.

$$Re(7\times 3+7\times \left(-5i\right)+\left(4-2i\right)\left(-6+7i\right))$$

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

$$Re(21-35i+\left(4-2i\right)\left(-6+7i\right))$$

Multiply complex numbers 4-2i and -6+7i like you multiply binomials.

$$Re(21-35i+4\left(-6\right)+4\times \left(7i\right)-2i\left(-6\right)-2\times 7i^{2})$$

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

$$Re(21-35i+4\left(-6\right)+4\times \left(7i\right)-2i\left(-6\right)-2\times 7\left(-1\right))$$

Do the multiplications in 4\left(-6\right)+4\times \left(7i\right)-2i\left(-6\right)-2\times 7\left(-1\right).

$$Re(21-35i-24+28i+12i+14)$$

Combine the real and imaginary parts in -24+28i+12i+14.

$$Re(21-35i-24+14+\left(28+12\right)i)$$

Do the additions in -24+14+\left(28+12\right)i.

$$Re(21-35i+\left(-10+40i\right))$$

Combine the real and imaginary parts in 21-35i-10+40i.

$$Re(21-10+\left(-35+40\right)i)$$

Do the additions in 21-10+\left(-35+40\right)i.

$$Re(11+5i)$$

The real part of 11+5i is 11.

$$11$$