If z1,z2 and z3 are complex numbers such that |z1|=|z2|=|z3|=∣∣∣1z1+1z2+1z3∣∣∣=1, then |z1+z2+z3| is
A
equal to 1
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B
less than 1
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C
greater than 3
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D
equal to 3
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Solution
The correct option is A equal to 1 |z1|=|z2|=|z3|=1 (given) Now |z1|=1⇒|zr|2=1 ⇒z1¯z1=1 Similarly z2¯z2=1,z3¯z3=1 Now ∣∣∣1z1+1z2+1z3∣∣∣=1 ⇒|¯z1+¯z2+¯z3|=1 ⇒|¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯z1+z2+z3|=1⇒|z1+z2+z3|=1