Question

Perform the indicated operation. 6-7i/6 + i

Answer 1

Answer: (28/37) - (48/37)*i

Step-by-step explanation:

We want to solve the quotient:

$\frac{6 - 7*i}{6 + i}$

To solve it, we need to multiply the whole quotient by the complex conjugate of the denominator.

Remember that for a complex number:

a + b*i

the complex conjugate is:

a - b*i

Then if the denominatoris:

6 + i

the complex conjugate is:

6 - i

Then to solve the quotient we have:

$\frac{6 - 7*i}{6 + i} *\frac{6 - i}{6 - i} = \frac{(6 -7*i)*(6 - i)}{(6 + i)*(6 - i)} = \frac{6*6 -7*6*i - 6*i + (-7*i)*(-i)}{6*6 +6*i - 6*i -i^2}$

This is equal to:

$\frac{6*6 -7*6*i - 6*i + (-7*i)*(-i)}{6*6 +6*i - 6*i -i^2} = \frac{36 - 42*i - 6*I - 7}{36 + 1} = \frac{29 - 48*i}{37}$

Then the initial quotient is equal to:

(28/37) - (48/37)*i