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>
Answer:
C
Explanation:
It prevents other variables such as independent variables and extraneous variables from affecting the validity of results. It also makes it easier to compare results when variables are changed.
Hope this helps :)
Answer:
Large birds can't fly due to higher weight and weak wings.
Why large birds can't fly?
Large birds like pheasants often walk short distances whereas small birds like chickadees never walk but fly because the large birds have more weight which can't support by the wings to fly in the sky so they walk on the land instead of flying.
While on the other hand, small birds have lower weight and easily fly in the sky so they don't need to walk on the ground so we can conclude that large birds can't fly due to higher weight and weak wings.
Explanation:
Answer:
<span>Leonard Howell and </span><span>Joseph Hibbert.</span>
The Gulf Stream simply means the strong ocean current which brings warm water from the Gulf of Mexico till it gets to the Atlantic Ocean.
Your information is incomplete. Therefore, an overview of the topic will be given. It should be noted that the Gulf Stream is a warm ocean current that is in the Western North Atlantic Ocean.
Global warming simply means the long-term heating of the Earth. It's the long-term shift in the weather patterns. This can be a result of the burning of fossil fuels which then produce heat-trapping gases.
Learn more about global warming on:
brainly.com/question/3553382