Hriday V.

asked • 06/16/20

Algebra 2 homework help

If  6 + 4i/1 - 3i = a + bi, what is the value of a + b

Lois C.

tutor
From the way that you wrote the problem, I took the 1 to be the only denominator ( which seemed a bit odd to me). Is the entire expression of 1 - 3i the denominator in this problem? If so, then both numerator and denominator need to be multiplied by the conjugate of the denominator, which is 1 + 3i. For the remainder of the problem, see my answer below.
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06/16/20

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Lois C. answered • 06/16/20

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If you combine the "i" terms in the original expression, you get 6 + 1i. Since this is now in a + bi form, the "a" value is 6 and the "b" value is 1, so the value of a + b is 6 + 1 or 7.

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Lois C.

tutor
Assuming that 1 - 3i is the entire denominator, we multiply top and bottom by the conjugate of the denominator, and so the numerator becomes 6 + 18i + 4i + 12i^2, which simplifies to -6 + 22i. The denominator becomes 1 + 3i - 3i -9i^2, which simplifies to 10. So the fraction is now (-6 + 22i)/10 which, in a + bi form, gives you an "a" value of -6/10 or -.6 and a "b" value of 2.2, so the sum of a + b is 1.6.
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06/16/20

Lois C.

tutor
Please also note: anytime you are dealing with i^2, its value is always -1.
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06/16/20

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