Real and imaginary parts of an expression

AI Thread Summary
To find the real and imaginary parts of the function (x + iy) * Log(a + ib), first apply the logarithmic identity Log(z) = ln|z| + iArg(z). This allows for the separation of the expression into its components. The magnitude |a + ib| can be calculated as sqrt(a^2 + b^2), and the argument Arg(a + ib) is arctan(b/a). By substituting these values into the original expression, the real part can be derived from the product of the real components, while the imaginary part arises from the product of the imaginary components. This method effectively simplifies the extraction of the real and imaginary parts of the given function.
Physicslad78
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can anyone tell me how to get the real and imaginary parts of the following function :

(x+ i y)* Log( a+i b) where x, y a and b are all real numbers and i =sqrt (-1).

Thanks very much
 
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Recall that Log(z) = ln|z| + iArg(z). When you write it like that, it is easy to separate the expression into real and imaginary parts.
 

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