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

1 Answer

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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

User Abhishek Tiwari
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