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Math Help - Complex Number

  1. #1
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    Complex Number

    Calculate the real part, the imaginary part, and the absolute value of the following expression:

    i * [(1+2i)(5-3i)+3i/(1+i)].


    So I did the math out this way:

    (1+2i)(5-3i)= 11+7i
    (11+7i)+3i/(1+i)= (4+21i)/(1+i)
    i * [(4+21i)/(1+i)] = (4i-21)/(1+i)

    Is this correct and what do you call the imaginary part and the real part if a denominator exists with an imaginary i?

    Thanks for any help.
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  2. #2
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    (1+2i)(5-3i)= 11+7i is correct!
    You should then rewrite 3i/(1+i)= (3i)(1-i)/2 = (3+3i)/2
    i[(11+7i)+ (3+3i)/2]=(-7+11i)+(-3+3i)/2 =(-17/2)+(25/2)i
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  3. #3
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    I really appreciate the help Plato. I was going to ask how the second part worked but I figured it out. You just multiply it by its conjugate.

    Thanks anyway.
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  4. #4
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    That really is an important point.
    In general, we do not allow complex numbers written as 1/(a+bi).
    In fact, the multiplicative inverse is, (a+bi)^(-1) = (a-bi)/(a^2+b^2).
    That is the conjugate divided by the absolute value squared.
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