I need some help drawing the following loci (which are rather hard to comprehend for me how will they look like) on an argand diagram:

  1. $$\arg \frac{i-z}{z+i}=\frac{\pi}{2} $$ (this one I suppose is simply an imaginary axis? due to the angle being pi/2)

  2. $$|z-i|+|z+i|=16$$ I don't quite understand this at all, is this a distance between two circles, where their radiuses depend on each other?

I have recently finished the loci of complex numbers on my Foundation course, yesterday I got these 2 and I can't for the life of me figure them out. Any help would be appreciated.


The second one is an ellipse with foci at $\pm i$.

For the first one, $i - z$ and $z + i$ are diagonals of a parallelogram. If $|z| = 1$, this parallelogram is a rhombus. The diagonals of a rhombus are perpendicular.

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