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Math Help - Complex numbers

  1. #1
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    Complex numbers

    The question:

    Simplify (\sqrt{3 + 4i}+\sqrt{3-4i})^2 where we assume \sqrt{z} has a non negative real part.

    My attempt:

    (3+4i) + 2(9-16i^2) + (3-4i) (perfect square)

    3 + 4i + 18 + 32 + 3 - 4i

    = 56

    That's not the answer though, it's supposed to be 16. I'm not sure what I'm going wrong. Any assistance would be great!
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  2. #2
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    Quote Originally Posted by Glitch View Post
    The question:

    Simplify (\sqrt{3 + 4i}+\sqrt{3-4i})^2 where we assume \sqrt{z} has a non negative real part.

    My attempt:

    (3+4i) + 2(9-16i^2) + (3-4i) (perfect square)

    3 + 4i + 18 + 32 + 3 - 4i

    = 56

    That's not the answer though, it's supposed to be 16. I'm not sure what I'm going wrong. Any assistance would be great!

    Who knows what you did here: (\sqrt{a}+\sqrt{b})^2=a+2\sqrt{ab}+b^2 , and you did something different (I think though

    that you forgot the square root in the middle term), so

    (\sqrt{3 + 4i}+\sqrt{3-4i})^2=3+4i+2\sqrt{9+16}+3-4i=3+10+3=16 , since 9-16i^2=9+16

    Tonio
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  3. #3
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    Quote Originally Posted by Glitch View Post
    The question:

    Simplify (\sqrt{3 + 4i}+\sqrt{3-4i})^2 where we assume \sqrt{z} has a non negative real part.

    My attempt:

    (3+4i) + 2(9-16i^2) + (3-4i) (perfect square)

    3 + 4i + 18 + 32 + 3 - 4i
    The middle term is wrong. You should still have a square root- it should be 2\sqrt{9- 16i^2}= 2(5), not 2(5)(5).

    = 56

    That's not the answer though, it's supposed to be 16. I'm not sure what I'm going wrong. Any assistance would be great!
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  4. #4
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    Thanks! I can't believe I missed that!
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