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)/(1-Z)

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 didnt 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 (3i-1.25)/(13/4)

= (12i-5)/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!

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