Question

What are the rules for determini ng Argument Quadrant ?

Answer 1

In these notes, we examine the argument of a non-zero complex number z, .... the four quadrants of the complex plane separately. .... We add two additional rules to the concept.

Answer 2

✔️When we represent a complex number

( z = x + iy)
... geometrically then the angle θ which the complex number makes with x axis is known as argument or amplitude of z and is denoted by arg (z) in amp(z).

✔️The argument θ which satisfies the inequality – π < θ ≤ π is usually known as principal argument of z.The argument of z depends upon the quadrant in which the point representing the complex number lies.

✔️Consider the complex number z = x + iy. Let P(x, y) represent the complex number z = x + iyin argand plane.


✔️If P(x, y) lies in 1st quadrant, then arg (z) = α
If P(x, y) lies in 2nd quadrant, then arg (z) = π – α


✔️If P(x, y) lies in 3rd quadrant, then arg (z) = π + α
If P(x, y) lies in 4th quadrant, then arg (z) = 2π – α

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