<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>.
Yes, (3, 2) is a solution to y = 2x - 4. (:
Answer:
Amount invested at 8% is $9000 and amount invested at 18% is $21000.
Step-by-step explanation:
Let amount invested at 8% be x.
Let amount invested at 18% be y.
We get the 1st equation as:
........(1)
We get the second equation as:
=> 
or getting rid of the decimal by multiplying by 100 on both sides.
........(2)
Multiplying (1) by 8 and subtracting from (2) we get
So, y = 21000
And 
So, x = 9000
Therefore, amount invested at 8% is $9000 and amount invested at 18% is $21000.
