Complex Numbers
Roots of Unity
Grade Class 11

Question:

<p>The diagram shows several numbers in the complex plane; the circle is the unit circle centred at the origin. One of the labeled numbers is the reciprocal of \( F \). Which one?</p>
A
B
C
D

Step-by-Step Solution

Key Concept: For a complex number z on or off the unit circle, its reciprocal 1/z = z̄/|z|^2 is the reflection across the real axis divided by |z|^2.
<p>If $ F $ has modulus $ r $ and argument $ \theta $, then $ 1/F $ has modulus $ 1/r $ and argument $ -\theta $. Reflecting across the real axis and inverting the modulus gives the point C.</p>
Correct Answer: C

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