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Math Help - Can someone check my Trig (Trig Form and Demoive's Theorm

  1. #1
    Junior Member
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    Can someone check my Trig (Trig Form and Demoive's Theorm

    Hi can someone check this to see if it's correct.

    Trig Form

    (4-3i) into Trig form

    r= Sqrt (4^2+(-3)^2
    r= Sqrt (25)
    r= 5

    tan = -(3/4) = -.01309
    arctan = -.74995
    2pi -.74995
    = 5.5332

    Z= 5 (cos 5.5332 + i sin 5.5332)
    ---------------------------
    I got confused with the Demoive question

    (11+i)^6

    r= Sqrt (11^2+1)
    r= Sqrt (122)

    tan 1/11 = .001586 <----- Is this right?
    arctan (.001586) = .09087103
    2pi + .09087103
    = 6.19231

    Put it into Trig form
    Z= Sqrt(122) (cos 6.19231 + i sin 6.19231)

    Demoiver's

    z^6 = Sqrt (122)^6 (cos 6.19231 + i sin 6.19231) ......

    First I don't even know if that is right. Also, if it is right I do not know the next step to completing the problem.

    Thanks
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  2. #2
    MHF Contributor
    Joined
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    Quote Originally Posted by killasnake
    Hi can someone check this to see if it's correct.
    (4-3i) into Trig form

    r= Sqrt (4^2+(-3)^2
    r= Sqrt (25)
    r= 5

    tan = -(3/4) = -.01309
    arctan = -.74995
    2pi -.74995
    = 5.5332

    Z= 5 (cos 5.5332 + i sin 5.5332)

    I got confused with the Demoive question

    (11+i)^6

    r= Sqrt (11^2+1)
    r= Sqrt (122)

    tan 1/11 = .001586 <----- Is this right?
    arctan (.001586) = .09087103
    2pi + .09087103
    = 6.19231

    Put it into Trig form
    Z= Sqrt(122) (cos 6.19231 + i sin 6.19231)

    Demoiver's

    z^6 = Sqrt (122)^6 (cos 6.19231 + i sin 6.19231) ......

    First I don't even know if that is right. Also, if it is right I do not know the next step to completing the problem.

    Thanks
    1)
    So you're saying that the trig form is z = r cis theta.

    You found r to be 5.
    You faultered on the theta.
    tan(theta) = -3/4 = -0.75 --------not -0.01309.
    So, theta = arctan(-0.75) = -0.6435 radians.
    Therefore, (4,-3i) = 5 cis (-0.6435rad) ---------------answer.
    Or, if you want positive theta,
    theta = -0.6435 == 2pi -0.6435 = 5.6397 radians
    Hence, (4,-3i) = 5 cis 5.6397rad -------------answer.

    Check,
    4 =? 5cos(5.6397 rad)
    Yes, so, OK.
    ---------------------------
    2)
    You're having problem with your theta.
    What is tan (1/11)? The (1/11) is a ratio, not an angle.
    It shoud be tan(theta) = 1/11.
    Then theta = arctan(1/11) = arctan(0.09090909...) = 0.09066 radian
    So, 11 +i = sqrt(122) cis 0.09066
    Then,
    (11 +i)^6
    = [sqrt(122)]^6 cis (0.09066 *6)
    = (122^3) cis 0.54396rad --------------answer.
    Last edited by ticbol; April 21st 2006 at 09:52 AM.
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  3. #3
    Junior Member
    Joined
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    Thanks for answering my question ticbol.
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