Math

[1337 k4th0l1x0r]

Yeah, you multiply the numerator and the denominator by 5+3i. Just do a quadratic expansion for both the numerator and denominator, that is, use the form (a+b)(c+d) = ac+bc+ad+bd. Remember that i*i=-1. Then group your terms on the numerator and divide by the denominator, which should be a real number.

Ask if you need clarification, or a hint at a first step.

Edited May 26, 2004 by 1337 k4th0l1x0r

[He carries me]

think i found it, hold on a sec

[RandomProddy]

Multiply the top and the bottom with the bottom's complex conjugate, so yep you were correct.

3+2i / 5-3i


= (3+2i)(5+3i) / (5-3i)(5+3i)

= 15 - 6 + i(10 + 9) / 25 + 9

=( 9 + 19i )/ 34

Edited May 26, 2004 by RandomProddy

[He carries me]

yeah i was just about to say that....

if you multiply it by 5+3i/5+3i, it stays the same because that's equal to one....

[cathgirl]

[quote name='1337 k4th0l1x0r' date='May 25 2004, 10:18 PM'] Yeah, you multiply the numerator and the denominator by 5+3i. Just do a quadratic expansion for both the numerator and denominator, that is, use the form (a+b)(c+d) = ac+bc+ad+bd. Remember that i*i=-1. Then group your terms on the numerator and divide by the denominator, which should be a real number.

Ask if you need clarification, or a hint at a first step. [/quote]
Don't think that this is right, but do you get

something / (25-6i^2) = something / (25 + 6) = something / 34

I'm not sure about the top

[RandomProddy]

[quote name='He carries me' date='May 26 2004, 04:22 AM'] yeah i was just about to say that....

if you multiply it by 5+3i/5+3i, it stays the same because that's equal to one.... [/quote]
Ya. Worth noting it won't work if the bottom is zero but it's unlikely you would get a question like that.

[cathgirl]

[quote name='RandomProddy' date='May 25 2004, 10:22 PM'] Multiply the top and the bottom with the bottom's complex conjugate, so yep you were correct.

3+2i / 5-3i


= (3+2i)(5+3i) / (5-3i)(5+3i)

= 15 - 6 + i(10 + 9) / 25 + 9

=9 + 19i / 34 [/quote]
So do ya get the i(10 + 9) ?

[cathgirl]

neva mind

[1337 k4th0l1x0r]

[quote name='cathgirl' date='May 25 2004, 09:24 PM'] Don't think that this is right, but do you get

something / (25-6i^2) = something / (25 + 6) = something / 34

I'm not sure about the top [/quote]
(3+2i)(5+3i) = 15+10i+9i+6(i^2)=15+19i-6=9+19i (this is the numerator)

(5-3i)(5+3i) = 25-9(i^2)=25+9=34

Final answer is 9/34+i19/34.

Though you could use matrices to solve this problem...