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Math Help - Final Proof

  1. #1
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    Final Proof

    For z, w \in \mathbb{C}, prove that z + w = w + z and zw = wz.

    My proof:

    Let z = a + ib and w = c + if

    Then, (a + ib) + (c + if) = (c + if) + (a + ib)

    (a + ib)(c + if) = ac + aif + ibc -bf and similarly for (c + if)(a + ib)

    Does this prove it?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Ideasman View Post
    For z, w \in \mathbb{C}, prove that z + w = w + z and zw = wz.

    My proof:

    Let z = a + ib and w = c + if

    Then, (a + ib) + (c + if) = (c + if) + (a + ib)

    (a + ib)(c + if) = ac + aif + ibc -bf and similarly for (c + if)(a + ib)

    Does this prove it?
    hehe, weird questions. it's hard to prove things that seem so obvious.

    for the addition i guest you could go the extra step and say by the commutative property of addition, you can rearrange the terms, and make it look exactly like the left hand side

    for the multiplication, i'd to as you do. consider the left hand side and expand. then consider the right hand side, and expand. show that you end up with the same expression after expanding
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