Regions in Argand Diagrams (Edexcel A-Level Further Mathematics): Flashcards

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Regions in Argand Diagrams
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What do regions represent in Argand diagrams

Sets of complex numbers satisfying particular conditions

What does modulus ∣z∣|z| represent geometrically

Distance from origin or another point

Region represented by ∣z−z1∣<r|z - z_1| < r

Inside circle, centre z1z_1, radius rr

Region represented by ∣z−z1∣>r|z - z_1| > r

Outside circle, centre z1z_1, radius rr

Boundary included in ∣z−z1∣<r|z - z_1| < r?

No

What does arg⁡(z)\arg(z) represent

Angle with the positive real axis

Region for α<arg⁡(z−z1)<β\alpha < \arg(z - z_1) < \beta

Sector between two rays at angles α\alpha and β\beta

Region for 0<arg⁡(z)<π20 < \arg(z) < \frac{\pi}{2}

First quadrant

Can modulus and argument conditions be combined?

Yes, to define more specific regions

Centre of circle in ∣z+2i∣>3|z + 2i| > 3

−2i-2i or point (0,−2)(0, -2)

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