Solve (2-bi)(7+bi)/1+i

$$\frac { ( 2 - b i ) ( 7 + b i ) } { 1 + i }$$

Evaluate

$$\left(\frac{1}{2}-\frac{1}{2}i\right)b^{2}+\left(-\frac{5}{2}-\frac{5}{2}i\right)b+\left(7-7i\right)$$

Solution Steps

Use the distributive property to multiply 2-bi by 7+bi.

$$\frac{7\left(2-bi\right)+i\left(2-bi\right)b}{1+i}$$

Multiply -1 and i to get -i.

$$\frac{7\left(2-ib\right)+i\left(2-bi\right)b}{1+i}$$

Multiply -1 and i to get -i.

$$\frac{7\left(2-ib\right)+i\left(2-ib\right)b}{1+i}$$

Use the distributive property to multiply 7 by 2-ib.

$$\frac{14-7ib+i\left(2-ib\right)b}{1+i}$$

Use the distributive property to multiply i by 2-ib.

$$\frac{14-7ib+\left(2i+b\right)b}{1+i}$$

Use the distributive property to multiply 2i+b by b.

$$\frac{14-7ib+2ib+b^{2}}{1+i}$$

Combine -7ib and 2ib to get -5ib.

$$\frac{14-5ib+b^{2}}{1+i}$$

Expand

$$\left(\frac{1}{2}-\frac{1}{2}i\right)b^{2}+\left(-\frac{5}{2}-\frac{5}{2}i\right)b+\left(7-7i\right)$$

Solution Steps

Use the distributive property to multiply 2-bi by 7+bi.

$$\frac{7\left(2-bi\right)+i\left(2-bi\right)b}{1+i}$$

Multiply -1 and i to get -i.

$$\frac{7\left(2-ib\right)+i\left(2-bi\right)b}{1+i}$$

Multiply -1 and i to get -i.

$$\frac{7\left(2-ib\right)+i\left(2-ib\right)b}{1+i}$$

Use the distributive property to multiply 7 by 2-ib.

$$\frac{14-7ib+i\left(2-ib\right)b}{1+i}$$

Use the distributive property to multiply i by 2-ib.

$$\frac{14-7ib+\left(2i+b\right)b}{1+i}$$

Use the distributive property to multiply 2i+b by b.

$$\frac{14-7ib+2ib+b^{2}}{1+i}$$

Combine -7ib and 2ib to get -5ib.

$$\frac{14-5ib+b^{2}}{1+i}$$