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piee

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complex number

Hi there ^_^
How are y'all doin?
I found a problem on complex numbers and i can't solve it. So can anyone help me pls?

Here's the problem:

You have a finite set of complex numbers z_1, ..., z_n, for which their polar forms z_j = r_j exp(i t_j) satisfy the constraint  0 <= |t_j| < phi < PI/2.

Show that cos(phi)|z_1 * z_2 * ... * z_n|^(1/n) <= 1/n * |z_1 + z_2 + ... + z_n|.

Thanks for your help in advance

Ps: i've tried to replace |z_1 * z_2 * ... * z_n|= |z_1| * |z_2| * ... * |z_n| and then replace them in their polar form.
And i found atgm rule but im still stuck on this pb