Answer to Question #27103 in Complex Analysis for PARTHA SAHOO
Show that Lagz can have real value if and only if < is positive
Recall that Log(z) is a multivalued function equal to Log(z) = ln(|z|)+ i Agr(z), where Arg(z) is the argument of z. Suppose for zome z Log(z) = ln(|z|)+ i Agr(z) is real value. This means that the imaginary part of Log(z) is zero, and so Agr(z) = 0. But this means that z belongs to the positive part of real axis, and so z is real and z>0. Conversely, suppose z>0. Then Arg(z)=0, whence Log(z) = ln(|z|) = ln(z) is real.
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