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Calculus

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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.

    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 -

    yeah...i did made an error...
    3.35 instead of 3.25...haha.
    thx guys!

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