Equations involving Argument of complex number and trigonometry

\[arg(\frac{z_1^3}{z_2^2})=arg(z_1^3)-arg(z_2^2)=3arg(z_1)-2arg(z_2)\]

where \[ z_1=a+ib\]  and \[z_2=c+id\]

Example- arg(\[ \frac{(1+i)^3}{(2+2i)^2}\]=3arg(\[ (1+i)\]-2*\[(2+2i)\]=\[3*45-2*45=45\] degrees

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