Pls show work/steps for both questions 1. Evaluate (-5+2i)/(1+7i). (Here i = √(-1).) Write in a + bi form. 2. Let f(x) = √(36-x^2). Find the domain and range of f(x). Write answ…

Question

Pls show work/steps for both questions

1. Evaluate
`(-5+2i)/(1+7i)`. (Here
`i = √(-1)`.)
Write in
`a + bi` form.

2. Let
`f(x) = √(36-x^2)`. Find the domain and range of f(x). Write answers in interval notation.

Answer 1

Explanation:

`(-5+2 \iota)/(1+7 \iota) * (1-7 \iota)/(1-7 \iota) \\=(-5+35 \iota+2 \iota-14 \iota^2)/(1-49 \iota^2) \\=(-5+37 \iota-14(-1))/(1-49(-1)) \\=(9+37 \iota)/(50) \\=(9)/(50) +(37)/(50) \iota`

2.

domain is x²≤36

|x|≤6

-6≤x≤6

or [-6,6]