Answer:
See proof below
Step-by-step explanation:
Let . If w=-z, then r=0 and r is real. Suppose that w≠-z, that is, r≠0.
Remember this useful identity: if x is a complex number then where is the conjugate of x.
Now, using the properties of the conjugate (the conjugate of the sum(product) of two numbers is the sum(product) of the conjugates):
=
Thus . From this, . A complex number is real if and only if it is equal to its conjugate, therefore r is real.
Answer:
13 inches
Step-by-step explanation:
Use the formula P = 2l + 2w to find width.
80 = 2(27) + 2w
80 = 54 + 2w
80 - 54= 2w
26 = 2w
w = 26/2
w = 13
The width of the rectangle is 13 inches.
Answer:
x = 5
Step-by-step explanation:
|2x + 6| = 16
=> 2x + 6 = 16
=> 2x = 16 - 6
=> 2x = 10
=> x = 5
Hoped this helped.
Answer:
4 months.
Step-by-step explanation:
33% is equal to 1/3. So when you take a third of 12, It comes out to 4.