Question

pls show work/steps for both questions
1. Evaluate $\frac{-5+2i}{1+7i}$. (Here $i = \sqrt{-1}$.)
Write in $a + bi$ form.

2. Let $f(x) = \sqrt{36-x^2}$. Find the domain and range of f(x). Write answers in interval notation.

Answer 1

Answer:

Step-by-step explanation:

$\frac{-5+2 \iota}{1+7 \iota} \times \frac{1-7 \iota}{1-7 \iota} \\=\frac{-5+35 \iota+2 \iota-14 \iota^2}{1-49 \iota^2} \\=\frac{-5+37 \iota-14(-1)}{1-49(-1)} \\=\frac{9+37 \iota}{50} \\=\frac{9}{50} +\frac{37}{50} \iota$

2.

domain is x²≤36

|x|≤6

-6≤x≤6

or [-6,6]