184k views
2 votes
Find the distance between 2-3i and 9+21i

Find the distance between 2-3i and 9+21i-example-1
User Celaxodon
by
8.7k points

2 Answers

5 votes

Answer:

25

Explanation:


d(z_1,\ z_2)=|z_1-z_2|\\\\z=a+bi\to|z|=√(a^2+b^2)\\------------------\\\\\text{We have:}\\\\z_1=2-3i,\ z_2=9+21i\\\\\text{substitute:}\\\\|(2-3i)-(9+21i)|=|2-3i-9-21i|\\\\=|(2-9)+(-3i-21i)|=|-7-24i|\\\\=√((-7)^2+(-24)^2)=√(49+576)=√(625)=25

User Rich Bryant
by
8.9k points
6 votes

Answer:

25.

Explanation:

For two complex numbers z=(
x_(1),y_(1)) and w=(
x_(2),y_(2)) we have that the distance between z and w is equal to

|z-w| =
\sqrt{(x_(1)-x_(2))^(2)+(y_(1)-y_(2))^(2)}

So, in this case we have that
(x_(1),y_(1))=(2,-3) and
(x_(2),y_(2))=(9,21), then the distance

|z-w| =
\sqrt{(2-9)^(2)+(-3-21)^(2)}

=
\sqrt{(-7)^(2)+(-24)^(2)}

=
√(49+576)

=
√(625)

= 25.

User Nixmd
by
8.7k points

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