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1)Let z1 and z2 be two complex no`s such that z1 not equal to z2 and |z1|=|z2|. If z1 has positive real part and z2 has negative imaginary part then (z1+z2)/(z1-z2) may be Answer-Zero and purely imaginary.How ??

1)Let z1 and z2 be two complex no`s such that z1 not equal to z2 and |z1|=|z2|. If z1 has positive real part and z2 has negative imaginary part then (z1+z2)/(z1-z2) may be Answer-Zero and purely imaginary.How ??

Grade:12th pass

1 Answers

mycroft holmes
272 Points
6 years ago
Let O be origin, A be z1, B be z2 and C be the point corresponding to z1+z2 on the complex plane. Then OAZB is a rhombus and z1+z2 and z1-z2 are the diagonals.
 
From geometry we know that the diagonals of a rhombus interesect at right angles. 
 
Hence arg (z1+z2/z1-z2) = 90 deg or – 90 deg i.e z1+z2/z1-z2 is purely imaginary

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