1.

Let z be a complex number of maximum amplitude satisfying `|z - 3| = Re(z)`, then `|z - 3|` is equal to

Answer» let` z= x+ iy`
`|z-3| = Re(z)``x^2 +9 -6x +y^2 = x^2``y^2= 6x-9``|z|= sqrt(x^2+ y^2)= sqrt(x^2 +6x-9)``d/dx(|z|)=0``(2x+6)/(2sqrt(x^2 + 6x-9))=0`
`x=-3`
`y^2= -6*3-9=-27`(Not possible)
So, x=3
y=3
Hence, `|z-3|= 3`


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