# Calculus

posted by .

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 -

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 -

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 -

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.

= (12i-5)/13 which is also drwls' answer

• Calculus -