1 + <em>i</em> + <em>i</em> ² + <em>i</em> ³ + <em>i</em> ⁴ + <em>i</em> ⁵ = 1 + <em>i</em> + <em>i</em> ² (1 + <em>i</em> + <em>i </em>² + <em>i</em> ³)
… = 1 + <em>i </em>+ <em>i</em> ² (1 + <em>i</em> + <em>i</em> ² (1 + <em>i</em> ))
… = 1 + <em>i</em> + (-1) (1 + <em>i</em> + (-1) (1 + <em>i</em> ))
… = 1 + <em>i</em> + (-1) (1 + <em>i</em> - 1 - <em>i</em> )
… = 1 + <em>i</em>
<em />
Alternatively, notice that
1 - <em>i</em> ⁶ = (1 - <em>i</em> ) (1 + <em>i</em> + <em>i</em> ² + <em>i</em> ³ + <em>i</em> ⁴ + <em>i</em> ⁵)
so that
1 + <em>i</em> + <em>i</em> ² + <em>i</em> ³ + <em>i</em> ⁴ + <em>i</em> ⁵ = (1 - <em>i</em> ⁶) / (1 - <em>i</em> )
Now, <em>i</em> ⁶ = (<em>i</em> ²)³ = (-1)³ = -1, so
1 + <em>i</em> + <em>i</em> ² + <em>i</em> ³ + <em>i</em> ⁴ + <em>i</em> ⁵ = (1 - (-1)) / (1 - <em>i</em> )
… = 2 / (1 - <em>i</em> )
Multiply the numerator and denominator by the conjugate of 1 - <em>i</em> :
… = 2 (1 + <em>i</em> ) / ((1 - <em>i</em> ) (1 + <em>i</em> ))
… = 2 (1 + <em>i</em> ) / (1² - <em>i</em> ²)
… = 2 (1 + <em>i</em> ) / (1 + 1)
… = 1 + <em>i</em>
The answer choice which is the correct description of the compositions of earth's different internal layers is:
- The Crust
- The Mantle
- The Core
<h3>The Earth</h3>
The earth is made up of various layers and the composition of the internal layers can be classified into the crust, mantle and core.
Each different layer has distinct features and characteristics which makes them unique and are important to preserve the Earth's core.
Read more about earth's internal layers here:
brainly.com/question/2673884
Answer:
mass of carbon monoxide
m = 36.55g
The chemical formula of carbon monoxide is,
C
O
.
Calculating the molar mass of carbon monoxide:
M
=
1
×
12
g
m
o
l
+
1
×
16
g
m
o
l
=
28
g
m
o
l
Calculating the number of moles:
n
=
m
M
=
36.55
g
28
g
m
o
l
=
1.305
m
o
l
Therefore, the are
1.305
moles in
36.55
grams of carbon monoxide
Answer:
a. alphabet line
Explanation:
Technical drawings are the drawings that help in communicating the designs. These designs are the designs that provide the instruction for the manufacturing of any object. The designs are made with the help of lines and line symbols. Line symbols are termed to be alphabet of lines. They help the designers to draw the designs with accuracy. Various lines are drawn that differ in terms of thickness and darkness. These variations helps the designers to mark the design accurately.
My friend flunked 8th grade but yet continued onto high school. But note, your parents can say yes to holding you back if a teacher recommends so. But other than that, you probably won’t get held back. But you will get held back in high school if you don’t pass.