Let $z=x+i?y$ , where $y>0$ . Choose a positive real number $t$ so that $t^2=x^2+y^2$ and pick positive numbers $u$ and $v$ satisfying $u^2=(t+x)/2 , v^2=(t-x)/2$ . Show that $x+i?y=(u+i?v)^2$ . Can you do a similar procedure of finding a square root if y is negative?
I am not exactly sure how to start this problem. Am I free to pick any t and start from there? Also, how can I show that $x+i?y=(u+i?v)^2$?
Do note that this is a community for questions about the Wolfram Language and related technologies. The three questions that you have recently posted are all asking advice in explaining concepts in mathematics. However you are not posting them as questions about Wolfram technologies.