Question

Z is a complex number, a is a constant. Find the maximum and minimum value of the complex number Z notice that :

Answer 1

\[\left| \frac{ 1 }{ Z } + Z \right| = a\]

Answer 2

a is not equal to zero

Answer 3

It's a complex number , you can assume it's A + Bi

Answer 4

It is.

Answer 5

No problem :D

Answer 6

the the max and min of what ?

Answer 7

of the complex number Z

Answer 8

how do we define the max of a complex number? do you mean the max magnitude ?

Answer 9

You can the maximum of A , B ( A+ Bi ) is the complex number.

Answer 10

Yeah, the magnitude

Answer 11

you could write Z= a exp( i x)
so Z+1/Z = a exp(ix) + (1/a) exp(-ix)
and the magnitude squared is
| Z+1/Z |^2 = (a exp(ix) + (1/a) exp(-ix))(a exp(-ix) + (1/a) exp(ix))
which might lead to a solution

Answer 12

Hmm, do you mean that e^x ? Never heard of it :(

Answer 13

no. I meant a complex number in polar coords is
magnitude * exp( i* theta)
btw, I should have used r instead of a, to not confuse the magnitude with the "a" given in your problem.

Answer 14

exp(i theta) means \( e^{i \theta}\)

Answer 15

Oh, Got it

Answer 16

Ok now we ave e^thetai + e^-thetai