In the form a+b where a and b are real numbers can anyone simplify (√(5) + 3i) / (1- i)?

Question

√(5) + 3i
-------------
1- i

Answer 1

multiply top and bottom by (1+i)

then you get

(sqrt (5) + 3i) * (1+i) / (1 - i^2) =
(sqrt (5) + 3i) * (1+i) / (1 + 1) =
(sqrt (5) + 3i) * (1+i) / 2 =
(sqrt (5) + 3i + sqrt(5)*i + 3i^2) / 2 =
(sqrt (5) - 3 + i (sqrt (5) + 3)) / 2 =
(sqrt(5) - 3) / 2 + [(sqrt (5) + 3) / 2] * i

Answer 2

= (√5 + 3 i).(1 + i) / (1 - i).(1 + i)
= (√5 + √5 i + 3i - 3) / (1 + 1)
= ((√5 - 3) + (√5 + 3) i ) / 2
= (√5 - 3) / 2 + (√5 + 3) i / 2
= - 0.38 + 2.62 i

Answer 3

if you have a ti83 or above, you can type this into your calculator.
anyway, it comes out to be root5/2-3/2+(root5/2+3/2)i