# Trouble in finding instances of values of variables that satisfy an inequality

Consider the following mathematical expression with complex numbers (phasor) and two variables (lambda and ia2):

0.10237519423935033 E^(-((0. + 5944.02363388283 I)/\[Lambda])+1/200 (-15 + 58.3 Log[0.493827 ia2]))


I make the absolute value of this expression and set an inequality like the following:

 Norm[0.10237519423935033 E^(-((
0. + 5944.02363388283 I)/\[Lambda]) +
1/200 (-15 + 58.3 Log[0.493827 ia2]))] > 0


Then I am trying to find the individual instances of lambda and ia2 with the given range that satisfy the inequality.

FindInstance[{Norm[
0.10237519423935033 E^(-((
0. + 5944.02363388283 I)/\[Lambda]) +
1/200 (-15 + 58.3 Log[0.493827 ia2]))] > 0, 1.52 < \[Lambda] < 1.58, 0.1 < ia2 < 40}, {\[Lambda], ia2}]


However, the following error pops up: FindInstance::nsmet: The methods available to FindInstance are insufficient to find the requested instances or prove they do not exist. >>

Can anyone help me fixing this error? Thanks.

• although the values of ia2 = 25; and [Lambda] = 1.55; clearly give the absolute value of this expression 0.1976 which is greater than 0. – Arafin Arif Jun 10 '15 at 18:27

## 1 Answer

Ahem, the norm of a Complex is always greater that zero ...

FindInstance[{Abs[ 0.10237519423935033 E^(-((0. +  5944.02363388283 I)/λ) +
1/200 (-15 + 58.3 Log[0.493827 ia2]))] > 0,
1.52 < λ < 1.58, 0.1 < ia2 < 40}, {λ, ia2}, 10]

(* {{λ -> 1.52188, ia2 -> 13.},
{λ -> 1.52314, ia2 -> 2.33333},
{λ -> 1.53602, ia2 -> 15.6667},
{λ -> 1.53614, ia2 -> 18.3333},
{λ -> 1.55161, ia2 -> 20.},
{λ -> 1.55508, ia2 -> 10.6667},
{λ -> 1.56114, ia2 -> 21.3333},
{λ -> 1.56485, ia2 -> 2.66667},
{λ -> 1.56719, ia2 -> 20.3333},
{λ -> 1.56761, ia2 -> 8.}}*)
`
• "greater than or equal to". ;) – J. M. is away Jun 10 '15 at 21:17
• @Guesswhoitis. "generally speaking":) – Dr. belisarius Jun 10 '15 at 21:50
• I have got one more question relating to it. If you want to set up the step size in the range of my given variable, how to modify the code? I mean, for 1.52 < λ < 1.58, if I want to fix the step size to 0.01, how to modify the above-mentioned code? Thanks. – Arafin Arif Jun 10 '15 at 22:35