Magnitude of complex numbers

Question

I'm working on a project that deals with complex numbers, to explain more (a + bi) where "a" is the real part of the complex number and "b" is the imaginary part of it. (a and b are real numbers but "i" isn't)

I'm having a hard time with implementing a magnitude method, instead of getting back a real number as a double i get infinity.

This is what I'm trying to implement: | (a + bi) | = √(a^2 + b^2)

a snippet off my code

public double mag(){
    /**
     * Compute the magnitude of this complex number.
     * 
     */
    //final double re is the real part
    //final double I'm is the imaginary part 
    double mag = Math.sqrt(Math.pow(this.re, 2) + Math.pow(this.im, 2));

    return mag;
}

say, if both real and imaginary numbers were Double.MAX_VALUE. why would mag return infinity instead of 1.8961503816218352E154 ?

Answer 1

Infinity numbers are numbers larger than Double.MAX_VALUE or smaller than -Double.MAX_VALUE. 1.0/0.0 is infinite. So is 2*Double.MAX_VALUE.

Math.pow(Double.MAX_VALUE,2) is obviously larger than Double.MAX_VALUE. Squaring of a largest possible number will result into something that regular number system can't represent.

Math.sqrt(Math.pow(this.re, 2) + Math.pow(this.im, 2))
==> Math.sqrt(Math.pow(Double.MAX_VALUE, 2) + Math.pow(Double.MAX_VALUE, 2))
==> Math.sqrt(Infinity + Infinity)
==> Infinity

Before the sqrt can be calculated, the squaring of a double max value resulted into infinity. you can't find sqrt of an Infinity number, so what you got it perfectly valid.