De Moivre's theorem uses this general formula z = r(cos α + i<span> sin α) that is where we can have the form a + bi. If the given is raised to a certain number, then the r is raised to the same number while the angles are being multiplied by that number.
For 1) </span>[3cos(27))+isin(27)]^5 we first apply the concept I mentioned above where it becomes
[3^5cos(27*5))+isin(27*5)] and then after simplifying we get, [243 (cos (135) + isin (135))]
it is then further simplified to 243 (-1/ √2) + 243i (1/√2) = -243/√2 + 243/<span>√2 i
and that is the answer.
For 2) </span>[2(cos(40))+isin(40)]^6, we apply the same steps in 1)
[2^6(cos(40*6))+isin(40*6)],
[64(cos(240))+isin(240)] = 64 (-1/2) + 64i (-√3 /2)
And the answer is -32 -32 √3 i
Summary:
1) -243/√2 + 243/√2 i
2)-32 -32 √3 i
Solving for <em>Angles</em>

* Do not forget to use the <em>inverse</em> function towards the end, or elce you will throw your answer off!
Solving for <em>Edges</em>

You would use this law under <em>two</em> conditions:
- One angle and two edges defined, while trying to solve for the <em>third edge</em>
- ALL three edges defined
* Just make sure to use the <em>inverse</em> function towards the end, or elce you will throw your answer off!
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Now, JUST IN CASE, you would use the Law of Sines under <em>three</em> conditions:
- Two angles and one edge defined, while trying to solve for the <em>second edge</em>
- One angle and two edges defined, while trying to solve for the <em>second angle</em>
- ALL three angles defined [<em>of which does not occur very often, but it all refers back to the first bullet</em>]
* I HIGHLY suggest you keep note of all of this significant information. You will need it going into the future.
I am delighted to assist you at any time.
Answer: 35/3 or 11.6
Step-by-step explanation:
3x-7=28
Add 7 to each side
3x=35
Divide by 3
Answer: 4/8 + 3/6 + 1/1
Step-by-step explanation: this is only if you can use the same number twice!!!