Let z1=r1(costheta1+isintheta1) and z2...

Let `z_1=r_1(costheta_1+isintheta_1)` and `z_2=r_2(costheta_2+isintheta_2)` be two complex numbers. Then prove that
`|z_1+z_2|^2=r_1^2+r_2^2+2r_1r_2cos(theta_1-theta_2)`
or
`|z_1+z_2|^2=|z_1|^2+|z_2|^2+2|z_1||z_2|^()_cos(theta_1-theta_2)` `|z_1-z_2|^2=r_1^2+r_2^2-2r_1r_2cos(theta_1-theta_2)` or
`|z_1-z_2|^2=|z_1|^2+|z_2|^2-2|z_1||z_2|^()_cos(theta_1-theta_2)`

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