Opposite of a complex question

[nhrock3]

(\frac{1}{0.81e^{j0.27}})*=\frac{1}{0.81}e^{j0.27}
why we can remove the constant?
why the conjugate of a complex number is multiplication of the angle by -1

 

[elibj123]

Complex conjugation is distributive over multiplication, and a real number is not affected by it, therefore you can pull the constant out.

The angle thing comes from euler's formula:

e^{j\theta}=cos(\theta)+jsin(\theta)

So

(e^{j\theta})*=cos(\theta)-jsin(\theta)=cos(-\theta)+jsin(-\theta)=e^{-j\theta}