Question

Find the distance d dd between z 1 = ( 6 + 2 i ) z 1 ​ =(6+2i)z, start subscript, 1, end subscript, equals, left parenthesis, 6, plus, 2, i, right parenthesis and z 2 = ( 6 + 10 i ) z 2 ​ =(6+10i)z, start subscript, 2, end subscript, equals, left parenthesis, 6, plus, 10, i, right parenthesis. Express your answer in exact terms and simplify, if needed. D =

Answer 1

8

Explanation:

Calculate the distance d using the distance formula

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

with (x₁, y₁ ) = z₁(6, 2) and (x₂, y₂ ) = z₂(6, 10)

d =
`√((6-6)^2+(10-2)^2)`

=
`√(0^2+8^2)`

=
`√(64)` = 8