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Is there a Better way to solve this complex inequality problem?
I have been asked to find the greatest and least values of |z+1| from the following equation
|z+1+2i|=2
The book I use suggests a method of drawing a circle and finding the highest value from the origin and the lowest value.
I hate when mathematics falls in diagrams.
Surely there is an algebraic way to do this?
The answers are 2sqrt2 +-2
I tried the triangle inequality but the answers came out different.
2 Answers
- DannyLv 46 years ago
Yes there is lmao.
If you have |x + 1| = 1
Can't you write it as x + 1 = 1 or x + 1 = -1? With complex numbers, this does not change!
|z - 1 + 2i| = 2
z - 1 + 2i = 2 or z - 1 + 2i = -2
z + 2i = 3 or z + 2i = -1
z = -2i + 3 or z = -2i - 1
You can also write it like that:
-1 = i²
z = 2i³ + 3 or z = 2i⁴
I don't know from where you got the other answers, but this is what I know.