Question 125695: Please help me solve: 6/i - 8/8-i. Combine and write the answer in standard form. Found 2 solutions by stanbon, solver91311:Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! 6/i - 8/8-i. Combine and write the answer in standard form
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[6(8-i)-8i]/[i(8-i)]
= [48-14i]/[8i+1]
Multiply numerator and denominator by (1+8i) to get:
= [2(24-7i)(1-8i)]/(64+1)
= [2(24-56-199i]/65
= (-64+398i)/65
= (-64/65)+ (398/65)i
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Cheers,
Stan H.
The first thing to do is rationalize the denominators, i.e. get the i out of each denominator and then you will be able to find a LCD to allow you to add the fractions.
The first fraction is easy, you just multiply by , giving you (remember )
The other fraction requires you to remember the factorization of the difference of two squares. . Using this, we could multiply the denominator of the second fraction, by its conjugate to obtain , but to do that we also have to multiply the numerator by the same thing. The result is that the second fraction looks like
(