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Math Help - Complex No. Qns

  1. #1
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    Complex No. Qns

    hi ,

    i got a question on complex no. How to prove the question is correct?

    | (3 + j4)^5 | = 5^5
    | ( 1 + j 3 ) | 2


    i know that |Z| = |x + jy| = sqrt (x^2 + y^2) = ( Z x Z*)

    for the lower part , i achieve ( 1 + 3 ) = 4 using ( Z x Z*) which i think i am right

    but i am stuck on the upper part. can't acheive the answer..

    (3 + j4)^5 which i can determine the r = 5 but am i on the right track converting into euler form ?

    Thanks a lot for any help
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  2. #2
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    Quote Originally Posted by Chris0724 View Post
    hi ,

    i got a question on complex no. How to prove the question is correct?

    | (3 + j4)^5 | = 5^5
    | ( 1 + j 3 ) | 2


    i know that |Z| = |x + jy| = sqrt (x^2 + y^2) = ( Z x Z*)

    for the lower part , i achieve ( 1 + 3 ) = 4 using ( Z x Z*) which i think i am right

    but i am stuck on the upper part. can't acheive the answer..

    (3 + j4)^5 which i can determine the r = 5 but am i on the right track converting into euler form ?

    Thanks a lot for any help
    Is this what you're asking?

    Show that
    \left|\frac{(3 + 4j)^5}{1 + 3j}\right| = \frac{5^5}{2}?
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  3. #3
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    Hi Chris0724

    Quote Originally Posted by Chris0724 View Post
    i know that |Z| = |x + jy| = sqrt (x^2 + y^2) = ( Z x Z*)
    This should be : |Z| = |x + jy| = sqrt (x^2 + y^2) = sqrt ( Z x Z*)

    for the lower part , i achieve ( 1 + 3 ) = 4 using ( Z x Z*) which i think i am right
    Maybe you want to recalculate this one ^^


    (3 + j4)^5 which i can determine the r = 5 but am i on the right track converting into euler form ?
    Yes, r = 5 is right. You don't have to state it in euler form if you want to find |(3 + j4)^5|

    But I don't think the question is right...
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  4. #4
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    Maybe this is the question?
    \frac{|(3 + 4j)^5|}{|1 + j{\color{red}\sqrt{3}}|} = \frac{5^5}{2}


    01
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  5. #5
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    Hi yeongil

    I believe so ^^
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  6. #6
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    Quote Originally Posted by yeongil View Post
    Maybe this is the question?
    \frac{|(3 + 4j)^5|}{|1 + j{\color{red}\sqrt{3}}|} = \frac{5^5}{2}


    01
    hi yes!! sorry for the typo error!! the question should be as above

    and yes! it should have been sqrt (Z x Z*)


    thanks!
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