Let z1=10+6i and z2=4+6i, where i=√−1. If z is any complex number such that arg(z−z1z−z2)=π4, then the value of |z−7−9i| is
A
2
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B
3
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C
2√3
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D
3√2
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Solution
The correct option is D3√2 Let z=x+iy
Then, z−z1z−z2=(x−10)+i(y−6)(x−4)+i(y−6) =[(x−10)+i(y−6)][(x−4)−i(y−6)](x−4)2+(y−6)2 =(x−10)(x−4)+(y−6)2(x−4)2+(y−6)2+i6(y−6)(x−4)2+(y−6)2