I was doing numericals on synchronous generators and came across this step in one of the examples. I have no idea what kind of math is used here. Can someone help?
$(1.5 + 2.0j)\Omega = 2.5 \angle 53.13^\circ \Omega$
$(0.3+1.22j)\Omega = 1.256 \angle 76.18^\circ\Omega$
These are two repesentations of complex numbers (in this case, used to define impedances- see Wikipedia for more info).
Also, note that in electrical engineering and related fields, the imaginary unit is represented as $j$ because the common representation of current is $i$.
Assuming you have a complex number $z$ represented in the cartesian form $a+jb$, you can transform it into other representations, such as polar representation: $$z=a+jb=R\cdot\mathrm{e}^{j\theta}$$ where $$R=|z|=\sqrt{a^2+b^2}\qquad \theta=\arg(z)=\arctan\biggl(\frac{b}{a}\biggr)$$
The representation you show (I do not know the proper name for this representation) is another polar representation, written differently: $$z=a+jb=R\cdot\mathrm{e}^{j\theta}=R\angle\theta$$ where, again, $$R=|z|=\sqrt{a^2+b^2}\qquad \theta=\arg(z)=\arctan\biggl(\frac{b}{a}\biggr)$$