If |z1−z0|=|z2−z0|=a and ampz2−z0z0−z1=π2, then z0 is equal to
A
12{(1+i)z1+(1−i)z2}
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B
12{(1−i)z1+(1+i)z2}
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C
12{z1+z2}
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D
None of the above
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Solution
The correct option is B12{(1+i)z1+(1−i)z2} We have, z2−z0z0−z1=eiπ2 ⇒z2−z0=iz0−iz1 ⇒z0(1+i)=z2+iz1 ⇒z0=12((1−i)(z2+iz1)) ⇒z0=12((1+i)z1+(1−i)z2) Hence, option A is correct