Back to Topic 1.12 — Complex numbers: Cartesian (HL only)
1.12.3Math AA HL8 flashcards

Modulus & the Argand diagram

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Card 1 of 81.12.3
1.12.3
Question

What is an Argand diagram?

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All 8 Flashcards — Modulus & the Argand diagram

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Card 1concept

Question

What is an Argand diagram?

Answer

The plane for complex numbers: real part across (horizontal), imaginary part up (vertical).

Card 2concept

Question

Where does z = a + bi sit on an Argand diagram?

Answer

At the point (a, b).

Card 3formula

Question

What is the modulus |z|?

Answer

The distance from the origin to z; |z| = √(a² + b²).

Card 4concept

Question

Why is |z| = √(a² + b²)?

Answer

It's Pythagoras — the point (a, b) is at horizontal distance a and vertical distance b from the origin.

Card 5concept

Question

|3 + 4i| = ?

Answer

√(9 + 16) = √25 = 5.

Card 6concept

Question

|5 − 12i| = ?

Answer

√(25 + 144) = √169 = 13.

Card 7concept

Question

Can the modulus be negative?

Answer

No — it's a distance, so |z| ≥ 0.

Card 8concept

Question

How does the sign of b affect the plot and the modulus?

Answer

It decides up (b > 0) or down (b < 0) on the diagram; the modulus is unaffected because b is squared.

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