Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

If z=a+bi, w=x+iy for a,b,x,y real, then what is the real part of zw?

3 Answers

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  • Philip
    Lv 6
    1 month ago

    z = (a+ib), w = (x+iy). zw = (a+ib)(x+iy) = (ax-by) + i(bx+ay). Real part of zw is

    (ax-by).

  • 1 month ago

    z = a + bi and w = x + yi

    So:

    zw

    Substitute and simplify:

    (a + bi)(x + yi)

    Multiply:

    ax + ayi + bxi + byi²

    i² = -1, so:

    ax + ayi + bxi - by

    Group the terms and factor out the "i":

    ax - by + ayi + bxi

    ax - by + (ay + bx)i

    the real part of "zw" is (ax - by)

    The imaginary part of "zw" is (ay + bx)

  • ted s
    Lv 7
    1 month ago

    a x - b y is the real part of the product zw

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