Discussion
Let \(z = x + iy\) be a complex number, where \(i = \sqrt{-1}\) is the complex unit. Then \(|z - 1 + i| = 5\) is a circle with
Answer: E
It is the circle with centre at (1,-1) and radius 5.
Write the condition as a distance: \(|z - z_{0}| = r\) is the circle of radius r about \(z_{0}\).
\[ |z - 1 + i| = |z - (1 - i)| = 5 \]
So the centre is the point \(1 - i\), that is (1, -1), and the radius is 5. Reading the centre as (-1, 1) flips both signs, and the options with radius \(\sqrt{5}\) or 25 confuse the radius with its square root or its square.
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