given z₁ and z₂, find the distance between them.
z₁ = 3 + 16i and z₂ = -6 + 4i
|z₁ - z₂| = ?

Question

given z₁ and z₂, find the distance between them.
z₁ = 3 + 16i  and  z₂ = -6 + 4i
|z₁ - z₂| = ?

Accepted Answer

# Explanation:
## Step1: Subtract $ z_2 $ from $ z_1 $
First, we calculate $ z_1 - z_2 $. Given $ z_1 = 3 + 16i $ and $ z_2 = -6 + 4i $, we have:
$$
\begin{align*}
z_1 - z_2&=(3 + 16i)-(-6 + 4i)\
&=3 + 16i + 6 - 4i\
&=(3 + 6)+(16i - 4i)\
&=9 + 12i
\end{align*}
$$
## Step2: Find the modulus of $ z_1 - z_2 $
The modulus of a complex number $ a + bi $ is given by $ \sqrt{a^2 + b^2} $. For $ z_1 - z_2 = 9 + 12i $, where $ a = 9 $ and $ b = 12 $, we calculate the modulus:
$$
\begin{align*}
|z_1 - z_2|&=\sqrt{9^2 + 12^2}\
&=\sqrt{81 + 144}\
&=\sqrt{225}\
& = 15
\end{align*}
$$
# Answer:
$ 15 $

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QUESTION IMAGE

Question

Explanation:

Step1: Subtract \( z_2 \) from \( z_1 \)

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

Answer: