A complex number ei + f can be divided into two factors: ai + b, where a and b are any two real numbers where a and b are not both
equal to zero, and ci + d, where c = (eb - fa)/(a^2 + b^2) and d = (ea + fb)/(a^2 + b^2)
13i + 18
e=13
f=18
c = (-18a + 13b)/(a^2 + b^2)
d = (13a + 18b)/(a^2 + b^2)
(ai+b)(ci-d)
a=2
b=0
c = (-18(2) + 13(0))/((2)^2 + (0)^2)
c = (-36)/(4)
c = -9
d = (13(2) + 18(0))/((2)^2 + (0)^2)
d = (26)/4
d = 6.5
(2i+0)(-9i-6.5)
-(18i^2)+13i+0+0
-(18*-1)+13i
-(-18)+13i
18+13i
13i+18
... Well hot damn. They said any two real numbers. I didn't think they meant you could just arbitrarily pick them.
Also, becasue this all became much easier:
-5
(2i-1)(2i+1)
4i^2-2i+2i-1
(4*-1)-1
-4-1
-5
How did the previous question become positive?! ... It was almost 6 in the morning. Typos do occur. Bite me.
Edit: Zem's answer is superior, because it has no decimals and is therefore, you know, legal. <p>
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Edited by: Besyanteo at: 11/18/05 14:06