Question

given $z_1$ and $z_2$, find the distance between them.
$z_1 = -20 + 17i$ and $z_2 = -10 + 14i$
$|z_1 - z_2| = \sqrt{?}$

Explanation:

Step1: Calculate \( z_1 - z_2 \)

Subtract the real and imaginary parts of \( z_2 \) from \( z_1 \) respectively.
\( z_1 - z_2 = (-20 + 17i) - (-10 + 14i) = (-20 + 10) + (17i - 14i) = -10 + 3i \)

Step2: Find the modulus of \( z_1 - z_2 \)

The modulus of a complex number \( a + bi \) is \( \sqrt{a^2 + b^2} \). For \( z_1 - z_2 = -10 + 3i \), we need to find \( (-10)^2 + 3^2 \).
\( (-10)^2 + 3^2 = 100 + 9 = 109 \)

Answer:

109