Question

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

Answer 1

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

Explanation:

We want to solve the quotient:

`(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:

`(6 - 7*i)/(6 + i) *(6 - i)/(6 - i) = ((6 -7*i)*(6 - i))/((6 + i)*(6 - i)) = (6*6 -7*6*i - 6*i + (-7*i)*(-i))/(6*6 +6*i - 6*i -i^2)`

This is equal to:

`(6*6 -7*6*i - 6*i + (-7*i)*(-i))/(6*6 +6*i - 6*i -i^2) = (36 - 42*i - 6*I - 7)/(36 + 1) = (29 - 48*i)/(37)`

Then the initial quotient is equal to:

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