If is a complex number with , what is the greatest possible value of ?
Answer and explanation
Correct answer: A.
- Step 1: Interpret the condition geometrically: describes a circle in the complex plane centered at with radius .
- Step 2: We wish to maximize the distance from on the circle to the point . The distance between the center and point is .
- Step 3: For any point on a circle, the maximum distance to an external point is .
Answer
.
Why not the others: is the minimum distance to the circle, and arises from an algebraic sign error in locating the circle center.
Practise more Complex numbers.
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