Question

How do you divide `(5/(1+i))`?

Answer 1

`1/2(5-5i)`

Explanation:

`"multiply the numerator/denominator by the complex"`
`"conjugate of the denominator"`

`"the conjugate of "1+i" is "1color(red)(-)i`

`=(5(1-i))/((1+i)(1-i))`

`=(5-5i)/(1-i^2)toi^2=-1`

`=(5-5i)/2=1/2(5-5i)`

Answer 2

`5/2(1-i)`

Explanation:

Given that

`5/{1+i}`

`={5(1-i)}/{(1+i)(1-i)}`

`={5(1-i)}/{1^2-i^2}`

`={5(1-i)}/{1-(-1)}\quad (\because \ i^2=-1)`

`={5(1-i)}/2`

`=5/2(1-i)`

Answer 3

`5/2(1-i)`

Explanation:

Dividing by complex numbers is the same as multiplying by the complex conjugate:

Complex Conjugate of a complex number `a+bi` is `a-bi`.

Multiplying by the complex conjugate, we now have

`(5(1-i))/((1+i)(1-i))`

`(5(1-i))/(1-i^2)`

Recall that `i^2=-1`. This all simplifies to

`5/2(1-i)`

Hope this helps!