SOLUTION: Express the following in terms of a + bi √5(2 + i) / 2 - i (3 - i)^2 / 2 + i Please solve this question. I am stuck in this ,don't know how to proceed further.

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Express the following in terms of a + bi √5(2 + i) / 2 - i (3 - i)^2 / 2 + i Please solve this question. I am stuck in this ,don't know how to proceed further.       Log On


   

Question 1117586: Express the following in terms of a + bi
√5(2 + i) / 2 - i
(3 - i)^2 / 2 + i
Please solve this question. I am stuck in this ,don't know how to proceed further.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Express the following in terms of a + bi
sqrt(5)(2 + i) / 2 - I
Assuming the DEN is 2-i
sqrt(5)(2 + i) /(2-i)
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Multiply the NUM and DEN by the conjugate of the DEN
= sqrt(5)(2 + i)*(2+i)/((2-i)*(2+i)
= sqrt(5)*(4 + 4i + i^2)/(4 - i^2)
= sqrt(5)*(4 + 4i - 1)/(4 + 1)
= sqrt(5)*(3 + 4i)/5
Or 3sqrt(5)/5 + (12sqrt(5)/5)i
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(3 - i)^2 / 2 + i
Same as above.
Add parentheses to the DEN