Which of the following represents
the set of complex numbers \(a+bi\) where
\(a,b\in\mathbb{R}\) and \(2|a|+|b| = 2\)?
(Hint: Try plotting a few complex numbers that satisfy the given condition.)
The answer is “a diamond”.
One could, for example,
come to this conclusion by plotting enough complex numbers to rule
out the other possibilites.
For example, the following complex numbers are sufficient for this purpose:
\(1\), \(-1\), \(2i\), \(-2i\), \(0.5+i\), \(0.5-i\), \(-0.5+i\),
\(-0.5-i\).