I have a rather annoying question in compex analysis. The question, I believe, should be solved without any use of advanced
compex analysis theorems or lemas, because it's in the first chapter in my book, so basic "calculus tricks" should suffice.
And for the problem : Let Z1,Z2 be two comlex numbers which fulfills : Z1/Z2 is not a real number (meaning the two vectors are not proportionate to one another), and Z2 is not 0 of course.
Prove that there's a real positive number - d>0 - that for each two real numbers x,y the following term will be fulfilled :
|xz1 + yz2| >= |x+y|
I'm really frustrated with that question, coming very close to solve at any time I take a different approach, but not there quite yet !
Any help/idea would be willingly recieved and appreciated.