Question

How can you find a complex number from a given absolute value?

Answer 1

For example, if I'm given the absolute value of 2, how do I find the complex number in terms of a+bi?

Answer 2

For an absolute value z,
\[z=\sqrt{a^2+b^2}\]
Then z² = a² + b²
But to find the expression a + bi I think that only the absolute value is not enough information.

Answer 3

I need to find an answer, not the only answer, so how I could set something up to find a possible solution?

Answer 4

You need the argument (the angle in the complex plane). Look at the image below: