Asked by Anne

two complex numbers Z and W are related by the formula
W=(Z+1)/(1-Z)

what is W if Z=1.5i?


thanks for the help!
Answered by drwls
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
Answered by Anne
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 !!!!
Answered by Reiny
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 (3i-1.25)/(13/4)
= (12i-5)/13 which is also drwls' answer

Check your work, you must have made an error.
Answered by Anne---?
yeah...i did made an error...
3.35 instead of 3.25...haha.
thx guys!
There are no AI answers yet. The ability to request AI answers is coming soon!