Question

(Find the distance between each of the following complex numbers. Give your answers in simplified radical form, and show all your work.)

1.) -1+i and -3-4i
2.) 1+i and 7-2i
3.) -3+4i and -6-i
4.) -2+3i and 2-2i
5.) 3 and 5+i
6.) -4+5i and 2-i

Thank you!

Answer 1

I) √29

ii) 3√5

iii) 5√5

iv) √41

v) √5

vi) 6√2

Explanation:

1)

Given complex numbers -1+i and -3-4i

The points are ( -1 , 1) and (-3 , -4 )

Distance formula

`\sqrt{(x_(2)-x_(1) )^(2) +(y_(2) -y_(1) )^2 }`

=
`\sqrt{(-4-(1) )^(2) +(-3 -(-1) )^2 } = √(25+4) =√(29)`

2)

Given complex numbers 1+i and 7-2i

The points are ( -3,4) and (-6,-1)

Distance formula

`\sqrt{(x_(2)-x_(1) )^(2) +(y_(2) -y_(1) )^2 }`

`\sqrt{(-2-1 )^(2) +(7-1)^2 } = √(9+36) =√(45)= 3√(5)`

3)

Given complex numbers -3 +4i and -6-i

The points are ( -3 ,4 ) and (-6 ,-1)

`\sqrt{(-1-4 )^(2) +(-6-4)^2 } = √(25+100) =√(125)= 5√(5)`

4)

Given complex numbers are -2+3i and 2-2i

The points are ( -2 ,3) and (2 , -2)

`\sqrt{(-2-3 )^(2) +(2+4)^2 } = √(25+36) =√(41)`



5)

Given complex numbers are 3 and 5+i

The points are( 3,0) and (5,1)

`\sqrt{(1-0 )^(2) +(5-3)^2 } = √(1+4) =√(5)`



6)

Given complex numbers are -4+5i and 2-i

The points are ( -4 ,5) and ( 2,-1)

`\sqrt{(-1-5 )^(2) +(2-(-4))^2 } = √(36+36) =√(72)= 6√(2)`