Answer: Imaginary axis (y-axis).
- A Circle of radius 3
- B Real axis
- C Imaginary axis (y-axis)
- D Line y = x
Correct answer: C. Imaginary axis (y-axis)
Explanation: Write z=x+iy. |z-3|=|x-3+iy|=√((x-3)²+y²); |z+3|=√((x+3)²+y²). Setting equal and squaring: (x-3)²+y²=(x+3)²+y². Expand: x²-6x+9=x²+6x+9, so -12x=0, x=0. Locus is the y-axis (imaginary axis). Answer: Imaginary axis (x = 0)
A complex number z = a+ib is plotted as a point (or vector from the origin) on the Argand plane, with the real part along the horizontal axis and the imaginary part along the vertical; its modulus |z| is the vector's length, and its argument θ is the angle from the positive real axis.
Concept context
Complex numbers in a+ib form, modulus, argument, polar form, cube roots of unity, and quadratic equations with complex roots
Read the full Complex Numbers and Quadratic Equations notes →