Posted by Anne on Thursday, March 13, 2008 at 7:15am.
two complex numbers Z and W are related by the formula
W=(Z+1)/(1Z)
what is W if Z=1.5i?
thanks for the help!

Calculus  drwls, Thursday, March 13, 2008 at 8:04am
Substitute 1.5i for Z in the equation.
W = (1 + 1.5i)/(1  1.5i)
This can be simplied by multiplying numerator and denominator by 1 + 1.5i. It gets rid of the complex deniminator. W = (1 + 1.5i)^2/(1 + 1.5)^2)
= (1/3.25)* (1 + 3i 2.25)
= (4/13)(1.25 + 3i)
= 5/13 + 12i/13 
Calculus  Anne, Thursday, March 13, 2008 at 8:24am
ah!!i was so dumb! i was trying to multiplying numerator and denominator by 1+Z,of course it didn't work out...haha...
thankyou !!!! 
Calculus  Reiny, Thursday, March 13, 2008 at 8:44am
Anne, you were not so dumb at all!
I solved the above question the same way by multiplying top and bottom by 1+Z.
Whether you substitute first and then multiply like drwls did, or multiply first and then substitute does not matter, you should get the same result.
I had (3i1.25)/(13/4)
= (12i5)/13 which is also drwls' answer
Check your work, you must have made an error. 
Calculus  Anne?, Thursday, March 13, 2008 at 9:53am
yeah...i did made an error...
3.35 instead of 3.25...haha.
thx guys!