Question

Which of the following complex numbers is
2-
equivalent to ? (Note: i= -1)
2+i

Answer 1

A

Explanation:

Given

`(2-i)/(2+i)`

Multiply the numerator/ denominator by the conjugate of the denominator.

The conjugate of 2 + i is 2 - i , then

=
`((2-i)(2-i))/((2+i)(2-i))` ← expand numerator/ denominator using FOIL

=
`(4-4i+i^2)/(4-i^2)` [ i =
`√(-1)` ⇒ i² = - 1 ]

=
`(4-4i-1)/(4+1)`

=
`(3-4i)/(5)`

=
`(3)/(5)` -
`(4)/(5)` i → A

Answer 2

i = the square root of -1

Explanation: