Points of the Argand plane
"Points of the Argand plane" is a free, interactive Class 11 Maths simulation for JEE, built on the lesson "The Argand plane" in Complex Numbers and Quadratic Equations. Drag the orange point: the point (a, b) is the complex number z = a + ib. The chips show its conjugate, its negative, or iz in purple. The faint circle has radius |z|. |z| is the distance from O; z̄ is the mirror image in the real axis; −z is opposite through O; iz is z turned 90° anticlockwise. All four points lie on the same circle of radius |z|. JEE Main asked 79 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
From the lesson The Argand plane in Complex Numbers and Quadratic Equations. Change the values and watch what happens.
In JEE Main
42 shifts analysed
79 questions from Complex Numbers and Quadratic Equations across the 42 JEE Main shifts Lumi has analysed (2017–2026).
The idea behind it
NCERT §4.5
- The complex number x + iy corresponds to the ordered pair (x, y), so it can be drawn as the point P(x, y) of the coordinate plane, and each point stands for exactly one complex number.
- A plane in which every point is read as a complex number is called the complex plane or the Argand plane. For example 3 + 4i, −2 + 3i, 5 and 2i sit at (3, 4), (−2, 3), (5, 0) and (0, 2).
- The x-axis carries the numbers a + i0 and is called the real axis; the y-axis carries the numbers 0 + ib and is called the imaginary axis.
- |x + iy| = √(x² + y²) is the distance of P from the origin O. So all the numbers with |z| = 5, such as 5, 3 + 4i, −4 + 3i and −5i, lie on the circle of radius 5 about O.
- The conjugate x − iy is the point Q(x, −y), the mirror image of P in the real axis. The negative −z = −x − iy is the point opposite P through O.
- The distance between the points z₁ and z₂ is |z₁ − z₂|. The distance from 1 + i to 4 + 5i is |3 + 4i| = 5.
- The signs of the parts fix the quadrant: −2 + 3i is in the second quadrant, −5 − 2i in the third and 1 − 2i in the fourth.
Questions
3 answers
- What does the "Points of the Argand plane" simulation show?
- Drag the orange point: the point (a, b) is the complex number z = a + ib. The chips show its conjugate, its negative, or iz in purple. The faint circle has radius |z|.
- Does JEE Main ask questions from Complex Numbers and Quadratic Equations?
- Yes. JEE Main asked 79 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
- Is this simulation free?
- Yes. It is free and runs in the browser on a phone or a laptop. It belongs to the lesson "The Argand plane" in Complex Numbers and Quadratic Equations (Class 11 Maths).
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