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CBSE Class 11-commerce Answered

If z1,z2, z3, z4 are complex numbers , show that they are vertices of a paralleogram in the Argand diagram if and only if z1+z3= z2 +z4.
Asked by vardhanishita9500 | 10 Jun, 2019, 06:23: PM
answered-by-expert Expert Answer
S u p p o s e space z subscript 1 comma space z subscript 2 comma space z subscript 3 comma space z subscript 4 space a r e space t h e space v e r t i c e s space o f space p a r a l l e log r a m
T h e r e f o r e comma space m i d p o i n t space o f space t h e space d i a g o n a l s space c o i n c i d e
rightwards double arrow fraction numerator z subscript 1 space plus space z subscript 3 over denominator 2 end fraction equals space fraction numerator z subscript 2 plus z subscript 4 over denominator 2 end fraction
rightwards double arrow z subscript 1 space plus space z subscript 3 equals space z subscript 2 plus z subscript 4
C o n v e r s e l y comma space a s s u m e space t h a t space z subscript 1 space plus space z subscript 3 equals space z subscript 2 plus z subscript 4
rightwards double arrow fraction numerator z subscript 1 space plus space z subscript 3 over denominator 2 end fraction equals space fraction numerator z subscript 2 plus z subscript 4 over denominator 2 end fraction
S o comma space w e space c a n space s a y space t h a t space t h e space m i d p o i n t space o f space t h e space d i a g o n a l s space c o i n c i d e
H e n c e comma space z subscript 1 comma space z subscript 2 comma space z subscript 3 comma space z subscript 4 space a r e space t h e space v e r t i c e s space o f space p a r a l l e log r a m
Answered by Renu Varma | 11 Jun, 2019, 10:54: AM

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