Minimum value

What have you tried so far? We need to see what you know, that you can use to solve the problem, since you will be the one solving it, not us.

My first thought is geometric: I visualized points z and z-1 on the complex plane, and what |z|+|z-1| would mean. That makes it easy to see what value(s) of z will minimize this.

But perhaps you are required to use algebraic methods. What happens if you replace z with x + iy? (This might require calculus, however; could you do that?)

It will be very helpful to know what topics you have been studying, specifically. Please follow the guidelines here.
 
Dr.Peterson said:
What have you tried so far? We need to see what you know, that you can use to solve the problem, since you will be the one solving it, not us.

My first thought is geometric: I visualized points z and z-1 on the complex plane, and what |z|+|z-1| would mean. That makes it easy to see what value(s) of z will minimize this.

But perhaps you are required to use algebraic methods. What happens if you replace z with x + iy? (This might require calculus, however; could you do that?)

It will be very helpful to know what topics you have been studying, specifically. Please follow the guidelines here.
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I'm sorry for not providing the complete details.The question is that If z is a complex number than what is the minimum vale of |z|+|z-1|? I have tried replacing z with x+yi and then z-1 with (x-1)+yi so for modulus I did It like that √(x²+y²) +√(x²+y²-1-2x) but I didn't seem to find the answer.
 
Sleeplesscoot said:
If z is any complex number then |z|+|z-1| has the minimum value of?
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Is it true that for any z\displaystyle z the expression ∣z∣+∣z−1∣\displaystyle |z|+|z-1| is a positive real number?
 
Since you didn't answer my question about context (that is, what you have learned that might be applicable), I can't tell whether your approach (the one I mentioned that could require calculus) is the best for you.

Try my graphical approach. Tell us what the geometrical interpretation is.
 
Sleeplesscoot said:
I'm sorry for not providing the complete details.The question is that If z is a complex number than what is the minimum vale of |z|+|z-1|? I have tried replacing z with x+yi and then z-1 with (x-1)+yi so for modulus I did It like that √(x²+y²) +√(x²+y²-1-2x) but I didn't seem to find the answer.
Click to expand...
We have a property: |z1|+|z2|>=|z1+z2|, hence |z|+|z-1|>=|z+1-z|=1, do you get this
 
Can you do a similar problem: Let z is a complex number such that |conjugate(z)+2i|<=|z-4i| and (z-3-3i)(conjugate(z)-3+3i). Find the maximum of |z-2|
 
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