<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>.
-5n - 3 - 3 > 19
-5n - 6 > 19
+ 6 +6
-5n > 25
divide by -5 on each side
change signs since dividing by negative
N< -5
For graphing on the line, you will create an OPEN circle on -5 and sketch it to the left.
Answer:
See below
Step-by-step explanation:
<u>Given function</u>
<u>We can find its factors:</u>
- x³ + 3x² - 7x - 21 =
- x²(x + 3) - 7(x + 3) =
- (x² - 7)(x + 3)
We can conclude that the given polynomial function is fully divisible by (x + 3) and the quotient is (x² - 7)
Also one of zeros of the function is -3
Answer: The answer would be f^-1 (x) = x/2 - 3/2
