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tatiyna
3 years ago
6

Use De Moivre’s Theorem to compute the following:

ula1" title="[3(cos27+isin27)}^5" alt="[3(cos27+isin27)}^5" align="absmiddle" class="latex-formula"> Please explain step by step how it works!
Mathematics
1 answer:
zhannawk [14.2K]3 years ago
4 0
Hello: 
<span>Use De Moivre’s Theorem : 
</span>(3(cos27 +isin27)^5 = 3^5( cos(27 × 5) +isin(27 × 5))
                                = 3^5 ( cos(135)+i sin(135))
                                = 3^5(-√2/2+i √2/2) 
because :  cos(135) = -√2/2    and   sin(135) = √2/2
(3(cos27 +isin27)^5 = (- 3^5√2/2)+ i ( 3^5√2/2)  ...(form : a+ib  when
a= (- 3^5√2/2)  and  b = ( 3^5√2/2)
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In circle A, ∠BAE ≅ ∠DAE. What is the length of BE? 14 units 17 units 27 units 34 units
zhannawk [14.2K]

Answer:

The length of BE is 27 units ⇒ 3rd answer

Step-by-step explanation:

In circle A:

∠BAE ≅ ∠DAE

Line segments A B, A E, and A D are radii

Lines are drawn from point B to point E and from point E to point D to form secants B E and E D

The length of B E is 3 x minus 24 and the length of E D is x + 10

We need to find the length of BE

∵ AB and AD are radii in circle A

∴ AB ≅ AD

In Δs EAB and EAD

∵ ∠BAE ≅ ∠DAE ⇒ given

∵ AB = AD ⇒ proved

∵ EA = EA ⇒ common side in the two triangles

- Two triangles have two corresponding sides equal and the

  including angles between them are equal, then the two

  triangles are congruent by SAS postulate of congruence

∴ Δ EAB ≅ Δ EAD ⇒ SAS postulate of congruence

By using the result of congruence

∴ EB ≅ ED

∵ EB = 3 x - 24

∵ ED = x + 10

- Equate the two expressions to find x

∴ 3 x - 24 = x + 10

- Add 24 to both sides

∴ 3 x = x + 34

- Subtract x from both sides

∴ 2 x = 34

- Divide both sides by 2

∴ x = 17

Substitute the value of x in the expression of the length of BE to find its length

∵ BE = 3 x - 24

∵ x = 17

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∴ BE = 51 - 24

∴ BE = 27

The length of BE is 27 units

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