Question
Question: The greatest and the least value of \|z<sub>1</sub> + z<sub>2</sub>\| if z<sub>1</sub> = 24 + 7i and...
The greatest and the least value of |z1 + z2| if z1 = 24 + 7i and |z2| = 6 are respectively
A
31, 19
B
25, 19
C
31, 25
D
None of these
Answer
31, 19
Explanation
Solution
Sol. Note that |z| = 6 represents a circle. As |z2| = 6,
|z1 + z2| = |z2 – (–24 – 7i)|
represent distance between a point on the circle |z| = 6 and the point C(– 24 – 7i).
|z1 + z2| will be greatest and least at points B and A which are the end points of the diameter of the circle through C.
As OC = 25, CA = OC – OA = 25 – 6 = 19 and
CB = OC + OB = 25 + 6 = 31.
