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Question

If z1,z2,z3 are complex numbers such that |z1|=|z2|=|z3|=1z1+1z2+1z3=1,then find the value of |z1+z2+z3|.


Solution

Given :

|z1|=|z2|=|z3|=1 |z1|2=|z2|2=|z3|2=1 z1¯¯¯¯¯z1=z2¯¯¯¯¯z2=z3¯¯¯¯¯z3=1 ¯¯¯¯¯z1=1z1,¯¯¯¯¯z2=1z2,¯¯¯¯¯z3=1z3Given that1z1+1z2+1z3=1 |¯¯¯¯¯z1+¯¯¯¯¯z2+¯¯¯¯¯z3|=1i.e.  |¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯z1+z2+z3|=1 |z1+z2+z3|=1


Mathematics
RD Sharma
Standard XI

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