A relation R on the set of complex numbers is defined by z_1 R z_2, if and only if z_1-z_2/z_1+z_...

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If for complex numbers `z_1 and z_2, arg(z_1) -arg(z_2)=0` then `|z_1-z_2|` is equal to If for complex numbers `z_1 and z_2, arg(z_1) -arg(z_2)=0` then `|z_1-z_2|` is equal to
If `z_1 and z_2` both satisfy the relation `z+overlinez=2|z-1| and arg(z_1-z_2)=pi/4,` then `I If `z_1 and z_2` both satisfy the relation `z+overlinez=2|z-1| and arg(z_1-z_2)=pi/4,` then `I
If z_1,z_2 and z_3 are three complex numbers satisfying 〖z_1〗^2+〖z_2〗^2+〖z_3〗^2-z_2 z_3-z_3 z_1-z... If z_1,z_2 and z_3 are three complex numbers satisfying 〖z_1〗^2+〖z_2〗^2+〖z_3〗^2-z_2 z_3-z_3 z_1-z...
|z_1*z_2|=|z_1|*|z_2| [Algebraic Proof, Further Pure Mathematics - Complex Numbers] |z_1*z_2|=|z_1|*|z_2| [Algebraic Proof, Further Pure Mathematics - Complex Numbers]
If z_1 and z_2 are two complex numbers satisfying the equation |z_1+z_2/z_1-z_2|=1, then z_1/z_2 ... If z_1 and z_2 are two complex numbers satisfying the equation |z_1+z_2/z_1-z_2|=1, then z_1/z_2 ...
`If z,z_1 and z_2` are complex numbers, prove that(i) `arg(barz)= - argz` (ii)`arg(z_1 z_2) = a... `If z,z_1 and z_2` are complex numbers, prove that(i) `arg(barz)= - argz` (ii)`arg(z_1 z_2) = a...
Prove that |z_1+z_2 |^2= |z_1 |^2+|z_2 |^2+2Re(z_1 z_2^* ) Complex Numbers Modulus Properties Prove that |z_1+z_2 |^2= |z_1 |^2+|z_2 |^2+2Re(z_1 z_2^* ) Complex Numbers Modulus Properties
If `z_1,z_2` and `z_3,z_4` are two pairs of conjugate complex numbers then `arg(z_1/z_4)+arg(z If `z_1,z_2` and `z_3,z_4` are two pairs of conjugate complex numbers then `arg(z_1/z_4)+arg(z