Question

What is the distance between (5 - 2i) and (8 + i)?

Answer 1

Answer:

Step-by-step explanation:

In complex plane we can see a+bi as the point (a,b).

so 5-2i can be seen as (5,-2)

and 8+i can be seen as (8,1)

Now we can use the distance formula to find the distance between the two points .

Distance formula is

$D=\sqrt{(x1-x2)^2+(y1-y2)^2}$

Plugging the respective values we get

$D= \sqrt{((5-8)^2+(-2-1)^2}\\D= \sqrt{(-3)^2+(-3)^2$

$D = \sqrt{9+9} \\D=\sqrt{18} \\D=3\sqrt{2}$

so Distance is $3\sqrt{2}$

Answer 2

Answer:

3√2

Step-by-step explanation:

We have to find distance between two points.

We represent a+bi as (a,b) on graph.

Hence, 5-2i can be represented as (5,-2).

and 8+i can be represented as (8,1).

By using distance formula, we can find distance between two points.

d=$\sqrt{(y_{2}-y_{1} )^{2} +(x_{2} -x_{1} )^{2}}$

d=$\sqrt{(1-(-2))^{2}+(8-5)^{2}}$

d=$\sqrt{(3)^{2} +(3)^{2} }$

d=$\sqrt{9+9}$

d=$\sqrt{18}$

d=$\sqrt{9.2}$

d=3√2 is distance between (5-2i) and (8+i).