if z1 z2 z3 z4 be the vertices of a square in the argand plane, then prove that 2z2=(1-i)z1+(1+i)z3

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Given, z1,z2,z3and z4 are the vertices of a square in the argand plane.To Prove: 2z2=1-iz1+1+iz3Proof:We need z2 in the form of z1 and z3. So, we rotate about B.Rotation about B in clockwise direction:z1-z2=z3-z2e-iπ2 z1-z2=z3-z2cosπ2-isinπ2z1-z2=z3-z2-iz1-z2=-iz3+iz2z1+iz3=z2+iz2z1+iz3=1+iz2z11+i+iz31+i=z2z11+i×1-i1-i+iz31+i×1-i1-i=z2z11-i2+i+1z32=z22z2=z11-i+1+iz3Hence Proved.
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