Question
Question: When \|Z\| = 1, the points 1 + 2Z lie on a...
When |Z| = 1, the points 1 + 2Z lie on a
A
Circle with radius 1 and centre (0, 1)
B
Circle with radius 2 and centre (1, 0)
C
Straight line
D
Circle with radius 3 and centre (1, 0)
Answer
Circle with radius 2 and centre (1, 0)
Explanation
Solution
Sol. Let W = 1 + 2Z. Then W –1 = 2Z
\ |W –1| = 2 |Z| = 2 for points on |Z| = 1
\ the locus of W is a circle with centre at (1, 0) and radius 2 when |Z| = 1