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Math Help - Complex simpification

  1. #1
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    Complex simpification

    How to simplify  \frac {3+4i}{5-2i} ? Thanks.
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    Quote Originally Posted by tttcomrader View Post
    How to simplify  \frac {3+4i}{5-2i} ? Thanks.
    Multiply both the numerator and the denominator by the complex conjugate of the denominator. ie:

     \frac{3+4i}{5-2i} \times \frac{5+2i}{5+2i}
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    Hello,
    Quote Originally Posted by tttcomrader View Post
    How to simplify  \frac {3+4i}{5-2i} ? Thanks.
    A conjugate of a complex number a+ib is defined to be a-ib
    What's good about it is if you multiply a complex number by its conjugate :
    (a+ib)(a-ib)=a^2+b^2 (using the identity (x-y)(x+y)=x-y) and that's a real number.

    So the main idea is to multiply both numerator and denominator by the conjugate of the denominator :

    \frac{3+4i}{5-2i}=\frac{3+4i}{5-2i} \cdot \frac{5+2i}{5+2i}=\frac{(3+4i)(5+2i)}{5^2+2^2}
    expand the numerator and separate real and imaginary parts.
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