If $z1 = 2 - i$ and $z2 = 1 + i$, what is the value of $\left|\frac{z1 + z2 + 1}{z1 - z2 + i}\right|$?

Question

Accepted Answer

Calculate numerator: $z1 + z2 + 1 = (2 - i) + (1 + i) + 1 = 4$. Calculate denominator: $z1 - z2 + i = (2 - i) - (1 + i) + i = 1 - i$. Thus, $\frac{4}{1 - i} = \frac{4(1 + i)}{2} = 2(1 + i)$. The modulus is $|2(1 + i)| = 2 \sqrt{1^2 + 1^2} = 2\sqrt{2}$.

Complex Numbers and Quadratic Equations

❓ Sibling Questions in this Chapter