<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>.
Answer:
Step-by-step explanation:
high school with pariantal consent
Reduce each ratio to its minimum expression to find if they are equal.
35:28
10:8
Since both ratios reduce to 5:4, they are equivalent.
Another way to check a:b is equivalent to c:d, is that a*d = b*c
In this case, this will be true if 35 times 8 is equal to 10 times 28:
Since both products are equal, then the ratios are equivalent.
Answer:
Step-by-step explanation:
Batman
Answer:
x² + 2x - 5
Step-by-step explanation:
(f + g)(x) = f(x) + g(x)
f(x) + g(x)
= 2x + 3 + x² - 8 ← collect like terms
= x² + 2x - 5
