Let z1=r1(costheta1+isintheta1)a n dz2=r...

Let `z_1=r_1(costheta_1+isintheta_1)a n dz_2=r_2(costheta_2+isintheta_2)` be two complex numbers. Then prove that `|z_1+z_2|^2=r1 2+r2 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=r1 2+r2 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)`

Similar Questions

Explore conceptually related problems

Let z_(1)=r_(1)(cos theta_(1)+i sin theta_(1)) and z_(2)=r_(2)(cos theta_(2)+i sin theta_(2)) be two complex numbers then prove the following

z_(1)bar(z)_(2)+bar(z)_(1)z_(2)=2|z_(1)||z_(2)|cos(theta_(1)-theta_(2))

If z_1 , and z_2 be two complex numbers prove that |z_1+z_2|^2+|z_1-z_2|^2=2[|z_1|^2+|z_2|^2]

For any two complex numbers z_1 and z_2 prove that: |\z_1+z_2|^2=|\z_1|^2+|\z_2|^2+2Re bar z_1 z_2

If z_1 and z_2 are two complex numbers, then prove that |z_1 - z_2|^2 le (1+ k)|z_1|^2 +(1+K^(-1) ) |z_2|^2 AA k in R^(+) .

if |(2iz_1-z_1-z_2)/(2iz_1-z_1-z_2)|=|(costheta+ isintheta)/(costheta-isintheta)| then prove that z_1/z_2 is purely real.

For any two complex numbers z_1 and z_2 , prove that |z_1+z_2| =|z_1|-|z_2| and |z_1-z_2|>=|z_1|-|z_2|

Let z_1,z_2 be complex numbers with |z_1|=|z_2|=1 prove that |z_1+1| +|z_2+1| +|z_1 z_2+1| geq2 .

For any two complex numbers z_1 and z_2 prove that: |\z_1+z_2|^2 +|\z_1-z_2|^2=2[|\z_1|^2+|\z_2|^2]