Answer:
6.403
Step-by-step explanation:
With imaginary units (defined by [tex]i[/tex]), the coordinate plane changes slightly. The x-axis is the axis for the "real" numbers, and the y-axis is what is used for the "imaginary" units.
Let's first take a look at both points:
2-4i
Since 2 is the "real" number and -4 is "imaginary" unit, we can make our first point: [tex](2, -4)[/tex]
6+i
There is an invisible 1 in front of the imaginary unit. Since 6 is the "real" number and 1 is the "imaginary", our second point will be [tex](6,1)[/tex]
Let's plug these into the distance between points formula:
[tex]\sqrt{ 6-2)^2+(1-(-4)^2\\[/tex]
[tex]= \sqrt{4^2}+ 5^2[/tex]
[tex]=\sqrt{16+25}[/tex]
[tex]\sqrt{41}[/tex]
[tex]=6.403[/tex]
Therefore, the distance between the two points is 6.403.
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