Confused about complex no

Hi can you help me with:

Suppose z = cis A where A is acute. Find the argument of z + 1:

I understand how to draw the vectors and all on the Argand diagram, so how the textbook showed it to be is the first picture.


However,t o find the argument of z+1, I don't understand, my understanding is that the argument of z+1 is the red angle, as shown in the next picture. Why is it wrong? For the answer is that the argument of z+1 is pi/2 since it is a rhombus, but I don't see how, not from my understanding of what a z+1 argument is!

Please help, thank you so much!
Thank you!

Quote:

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Originally Posted by Tutu

Suppose z = cis A where A is acute. Find the argument of z + 1: For the answer is that the argument of z+1 is pi/2 since it is a rhombus[/COLOR]

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That is not true.
You must have misread the question or have left something out.

Attachment 25971

This is the whole question, complete with solutions. I gathered from here that the argument of z+1 is pi/2. Read it over and still thought so. Maybe my understanding is not good enough..

Thank you!