Question

If z1, z2, z3 are three distinct complex number where|z1| = 1, |z2| = 3, |z3| = 4, and arg z2 = arg z1

Answer 1

Answer

An argument of the complex number z = x + iy, denoted arg(z), is defined in two equivalent ways: Geometrically, in the complex plane, as the angle φ from the positive real axis to the vector representing z. The numeric value is given by the angle in radians and is positive if measured counterclockwise.

Answer 2

If z1, z2, z3 are three distinct complex number where|z1| = 1, |z2| = 3, |z3| = 4, and arg z2 = arg z1.

Argument of a complex number can be defined as the angle of the vector z with the positive x axis.

| Z | is defined as the magnitude of the complex number.

if Z = x + iy , then

• | z | = $\sqrt{x^{2} + y^{2} }$

• arg ( z ) = $tan^{-1} \frac{y}{x}$

In the question | z1 | is not equal to | z2 |

But their argument is same.

Hence they are two complex numbers in the same direction with different magnitudes.