Complex Numbers & Argand Diagrams (Edexcel A-Level Further Mathematics): Quizzes

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Regions in Argand Diagrams
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What does ∣z−z1∣<r|z - z_1| < r represent on an Argand diagram?

Inside a circle, centre z1z_1, radius rr

Is the boundary included in the region ∣z−z1∣<r|z - z_1| < r?

No, not included

What is the centre of the circle represented by ∣z−(2+3i)∣<5|z - (2 + 3i)| < 5?

(2,3)(2, 3)

What does ∣z−z1∣>r|z - z_1| > r represent on an Argand diagram?

Outside a circle, centre z1z_1, radius rr

What is the radius of the circle in ∣z−(−1+2i)∣>3|z - (-1 + 2i)| > 3?

33

What does the argument of a complex number represent?

Angle with positive real axis

What does α<arg⁡(z−z1)<β\alpha < \arg(z - z_1) < \beta represent?

A sector between two rays

Which quadrant does 0<arg⁡(z)<π20 < \arg(z) < \frac{\pi}{2} represent?

First quadrant

What region is ∣z∣<4|z| < 4 and 0<arg⁡(z)<π20 < \arg(z) < \frac{\pi}{2}?

Inside circle radius 4, first quadrant

What is the centre of the circle in ∣z+2i∣>3|z + 2i| > 3?

(0,−2)(0, -2)

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