<em>z</em> = 3<em>i</em> / (-1 - <em>i</em> )
<em>z</em> = 3<em>i</em> / (-1 - <em>i</em> ) × (-1 + <em>i</em> ) / (-1 + <em>i</em> )
<em>z</em> = (3<em>i</em> × (-1 + <em>i</em> )) / ((-1)² - <em>i</em> ²)
<em>z</em> = (-3<em>i</em> + 3<em>i</em> ²) / ((-1)² - <em>i</em> ²)
<em>z</em> = (-3 - 3<em>i </em>) / (1 - (-1))
<em>z</em> = (-3 - 3<em>i </em>) / 2
Note that this number lies in the third quadrant of the complex plane, where both Re(<em>z</em>) and Im(<em>z</em>) are negative. But arctan only returns angles between -<em>π</em>/2 and <em>π</em>/2. So we have
arg(<em>z</em>) = arctan((-3/2)/(-3/2)) - <em>π</em>
arg(<em>z</em>) = arctan(1) - <em>π</em>
arg(<em>z</em>) = <em>π</em>/4 - <em>π</em>
arg(<em>z</em>) = -3<em>π</em>/4
where I'm taking arg(<em>z</em>) to have a range of -<em>π</em> < arg(<em>z</em>) ≤ <em>π</em>.
To solve this you must use the rules of PEMDAS (Parentheses, Exponent, Multiplication, Division, Addition, Subtraction)
In this problem we have double parentheses. Which one should we solve first? The answer to that is always the inner most ones:
13[ 6² ÷ (5² - 4²) + 9]
5² - 4²
^^^Here you will have to first take the square of both values
25 - 16
9
13[ 6² ÷ (9) + 9]
Now for the exponents
13[ 6² ÷ (9) + 9]
6²
36
13[ 36 ÷ 9 + 9]
Now for the division:
13[ 36 ÷ 9 + 9]
36 ÷ 9
4
13[ 4 + 9]
Now for the addition
13[ 4 + 9]
4 + 9
13
13[13]
Now for multiplication
169
Hope this helped!
~Just a girl in love with Shawn Mendes
point slope form of a line
y-y1 = m(x-x1)
y-7 = -2 (x-1)
if you want it in slope intercept form
y-7 = -2x +2
add 7 to each side
y = -2x +9
