Explain how you would find the square roots of 5+3i then use the method to find the roots of 5+3i
Please show all steps!
there are 2 ways, one is long and one is short,
The short one:
$\displaystyle
5 + 3i = \sqrt {34} e^{j\arctan \left( {\frac{3}
{5}} \right)}
$
$\displaystyle
\Rightarrow \sqrt {5 + 3i} = \sqrt[4]{{34}}e^{j\frac{1}
{2}\arctan \left( {\frac{3}
{5}} \right)} = \sqrt[4]{{34}}\left[ {\cos \left( {\frac{1}
{2}\arctan \left( {\frac{3}
{5}} \right)} \right) + j\sin \left( {\frac{1}
{2}\arctan \left( {\frac{3}
{5}} \right)} \right)} \right]$
and of course the second root:
$\displaystyle
\sqrt[4]{{34}}e^{j\frac{{\arctan \left( {\frac{3}
{5}} \right) + 2\pi }}
{2}}
$