I recently was confronted by this monstrosity of a question in one of my mock exams. |Z1 + Z2| ≤ |Z1| + |Z2| I made a few attempts at it before becoming demoralized with the lack of progress.. |Z^2| was equal to Z1(conjugate)Z1 Hence equaling X^2 + Y^2 However even when expanding into x+iy form etc no avail, help is appreciated.
square both side and see if you notice anything and remember if A=A then, surely A is less than or equal to A
Geometrically this is just the triangle inequality. It just says that the sum of two sides of a triangle is always greater or equal than the third. Since you know |z|^2=z*z. Why not write the left side out in this form? ie: |z+w|^2=(z*+w*)(z+w)
I'm sorry but I had to laugh when I read "I recently was confronted by this monstrosity of a question..." only to find the triangle inequality beneathe. lol.