<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>.
Given:
ft and 
ft.
To find:
The value of P.
Solution:
We have,
Substituting and , we get
Taking LCM, we get
Therefore, the value of P is 
ft.
For a logarithmic function, we have a restriction on the domain.
Since log(0) isn't defined, we say that there is an asymptote at x = 0.
Thus, for the regular logarithmic function y = log(x), x > 0.
We can then say (x + 4) > 0, since that's when the function of a logarithm is defined as.
x + 4 > 0
x > -4
Thus, the domain of the logarithmic function is x > -4, where x is a real integer.
Method 1:
Look at the picture.
is greater than 
Method 2:
Find the common denominator:
multiples of 7: 0, 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, ...
multiples of 9: 0, 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, ...
63 = 7 · 9
therefore
