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!
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
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 !!!!
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.
yeah...i did made an error...
3.35 instead of 3.25...haha.
thx guys!
To find the value of W when Z is given, we substitute the value of Z into the formula:
W = (Z + 1) / (1 - Z)
Given Z = 1.5i, we substitute it into the formula:
W = (1.5i + 1) / (1 - 1.5i)
Now, we need to simplify this expression by multiplying the numerator and denominator by the conjugate of 1 - 1.5i, which is 1 + 1.5i:
W = (1.5i + 1) * (1 + 1.5i) / (1 - 1.5i) * (1 + 1.5i)
Expanding the expression:
W = (1.5i + 1 + 1.5i + 2.25i^2) / (1 - 1.5i + 1.5i - 2.25i^2)
Since i^2 = -1, we can simplify the expression further:
W = (1.5i + 1 + 1.5i - 2.25) / (1 - (-2.25))
Simplifying again, combining like terms:
W = (3i - 1.25) / (3.25)
Dividing the numerator by the denominator, W becomes:
W = (3i - 1.25) / 3.25
Therefore, W is equal to (3i - 1.25) / 3.25 when Z = 1.5i.