Question

find the distance between
-1 - 2i
and
4 + 4i
\sqrt{?}

Explanation:

Step1: Identify coordinates

For complex number \( z_1 = -1 - 2i \), real part \( x_1 = -1 \), imaginary part \( y_1 = -2 \).
For \( z_2 = 4 + 4i \), real part \( x_2 = 4 \), imaginary part \( y_2 = 4 \).

Step2: Apply distance formula

Distance between \( (x_1,y_1) \) and \( (x_2,y_2) \) is \( \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \).
Calculate \( x_2 - x_1 = 4 - (-1) = 5 \), \( y_2 - y_1 = 4 - (-2) = 6 \).

Step3: Compute the radicand

Square the differences: \( 5^2 + 6^2 = 25 + 36 = 61 \).

Answer:

\( 61 \) (the value inside the square root is \( 61 \))