Q.
If z is a complex number, then ∣3z−1∣=3∣z−2∣ represents
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Complex Numbers and Quadratic Equations
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Solution:
Let z=x+iy, then ∣3z−1∣=3∣z−2∣ ⇒∣3(x+iy)−1∣=3∣x+iy−2∣ ⇒∣(3x−1)+3iy∣=3∣x−2+iy∣ ⇒(3x−1)2+9y2=9[(x−2)2+y2] ⇒9x2+1−6x+9y2 =9x2+36−36x+9y2 ⇒30x=35 ⇒x=67.
i.e., a st. line ∣∣ to y-axis.