PART 4 (IIT JEE Lecture Series – Complex Numbers | Maximum and Minimum Value)
In this video, I will discuss the method: how one can use triangle inequality to find the maximum or minimum value of a complex number. I will discuss four question in total out of which one came in AIEEE exam in the year 2007.
I will also discuss how triangle inequality can be extended to more than two complex numbers.
Triangle inequality Application to find maximum / minimum value:
|(|z_1 |-|z_2 |)| ≤ |z_1+z_2 | ≤ |z_1 |+|z_2 |
The above concepts are important for students studying for IIT JEE.
Question 1 [AIEEE 2007]
If |z+4|≤3, then the maximum value of |z+1| is
(A) 6 (B) 0 (C) 4 (D) 10
Question 2 (Doubt sent by student on email)
If |z-3+2i|=4,, find the difference between greatest and least value of |z|.
Question 3 (Triangle Inequality extended to more than two complex numbers)
Find the minimum value of |z|+|z-1|+|2z-3|.
Question 4 (Triangle Inequality extended to more than two complex numbers)
If |z_1-1|≤1,|z_2-2|≤2,|z_3-3|≤3, find the greatest value of |z_1+z_2+z_3 |.
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