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Math Help - Complex Numbers - Modulus

  1. #1
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    Complex Numbers - Modulus

    My question is: Find the modulus of ((15i)^4)/((-5-10i)^6)

    For this would the top line just be 15^4 = 50625.

    The bottom line: root 125 then to the power 6.

    Please help. Thanks
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  2. #2
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    you seem to do be doing well, know how to find the modulus of both the denominator and the numerator, now you just divide them.
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  3. #3
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    Okay thanks, I get 50625/1953125.
    This simplifies to 81/3125.

    The only problem I have is that this is practice question from a non-calculator test. Do you you know if there is an easier way to approach this with no calculator. Thanks.
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  4. #4
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    well the numbers in this question are fairly easy due to nice prime factors

     125 = 5^3
    15= 5 \cdot 3

    so your fraction is

     \frac{(5 \cdot 3)^4 } {(5^3)^3} \rightarrow  \frac{5^4 \cdot 3^4 } {5^9} \rightarrow \frac{3^4 } {5^5}

    so this can be done fairly easily without a calculator
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  5. #5
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    Thanks for your help
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