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Math Help - Find Value of c

  1. #1
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    Find Value of c

    The complex number
    c + di is equal to (2 + i)^2. What is the value of c?

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  2. #2
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    Quote Originally Posted by magentarita View Post
    The complex number
    c + di is equal to (2 + i)^2. What is the value of c?

    So we have

    c+di = (2+i)^2
    first, me must expand the quantity (2+i)^2 so let's do that

    (2+i)^2 = (2+i)(2+i)
                = 4+2i+2i+i^2
                = 4+4i-1
                = 3+4i

    So, we have

    c+di = 3+4i
    In complex numbers the real part must equate with the real part and the imaginary part must equate with the imaginary part in a complex number so c must equal 3 since it is the only real part of 3+4i.
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  3. #3
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    ok...........

    Quote Originally Posted by caelum View Post
    So we have

    c+di = (2+i)^2
    first, me must expand the quantity (2+i)^2 so let's do that

    (2+i)^2 = (2+i)(2+i)
     = 4+2i+2i+i^2
     = 4+4i-1
     = 3+4i

    So, we have

    c+di = 3+4i
    In complex numbers the real part must equate with the real part and the imaginary part must equate with the imaginary part in a complex number so c must equal 3 since it is the only real part of 3+4i.
    A job well-done!
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