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.

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.
Report

06/16/20

2 Answers By Expert Tutors

By:

Lois C. answered • 06/16/20

Tutor
5.0 (116)

patient, knowledgeable, and effective tutor for secondary mathematics

See tutors like this
See tutors like this

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.

Upvote • 0 Downvote
More
Report

Lois C.

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.
Report

06/16/20

Lois C.

Please also note: anytime you are dealing with i^2, its value is always -1.
Report

06/16/20

Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem.
Most questions answered within 4 hours.

OR

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.