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sattari [20]
2 years ago
8

What is the product of 65(cos(14°)+ i sin(14°)) and 8(cos(4°)+ i sin(4°))

Mathematics
1 answer:
saveliy_v [14]2 years ago
3 0

The product of the complex numbers 65(cos(14°)+ i sin(14°)) and 8(cos(4°)+ i sin(4°)) is 520[cos(18) + isin(18)]

<h3>What is an equation?</h3>

An equation is an expression that shows the relationship between two or more numbers and variables.

Complex number is in the form z = a + bi, where a and b are real numbers.

The product of the complex numbers 65(cos(14°)+ i sin(14°)) and 8(cos(4°)+ i sin(4°)) is:

z = 65 * 8 [cos(14 + 4) + isin(14 + 4)] = 520[cos(18) + isin(18)]

Find out more on equation at: brainly.com/question/2972832

#SPJ1

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What is the rectangular form of z= 40(cos(7pi/6)+ i sin(7pi/6))
Anastaziya [24]

Answer:

C. z = -20\sqrt{3}-i\,20

Step-by-step explanation:

The rectangular form of a complex number is represented by the following formula:

z = a+i\,b (1)

Where each coefficient can be determined as function of the polar components:

a = r\cdot \cos \theta (2)

b = r\cdot \sin \theta (3)

Where:

r - Magnitude of the complex number, dimensionless.

\theta - Direction of the complex number, measured in radians.

If we know that r = 40 and \theta = \frac{7\pi}{6}, then the rectangular form of the number is:

a = 40\cdot \cos \frac{7\pi}{6}

a = -20\sqrt{3}

b = 40\cdot \sin \frac{7\pi}{6}

b = -20

The rectangular form of z=40\cdot\left(\cos \frac{7\pi}{6}+i\,\sin \frac{7\pi}{6}\right) is z = -20\sqrt{3}-i\,20. The correct answer is C.

4 0
2 years ago
An equilateral triangle and an isosceles triangle share a common side. What is the measure of angle ABC?
o-na [289]

Answer:

Therefore ,the measure of angle ABC = 116°.

Step-by-step explanation:

Given:

Δ CBD is an Equilateral Triangle

BC = BD = CD

Δ ABD is an Isosceles Triangle

AB = BD

To Find:

m∠ ABC = ?

Solution:

Property For an Equilateral Triangle:

All the measure of Each of the angles angles of a triangle is 60°.

Δ CBD is an Equilateral Triangle   ..........Given

∴ m∠ CBD = 60° ....................( 1 )

Property For an Isosceles Triangle:

Any two of the base angles are equal.

Δ ABD is an Isosceles Triangle ................Given

∴ m∠ BAD = m∠ BDA = 62°  .....................( 2 )

Property of Triangle:

SUM of the measure of an angles of a triangle is 180°

In Δ BAD,

m∠ ABD + m∠ BAD + m∠ BDA = 180°

Substituting the values from equation ( 2 ) in it we get

m∠ ABD + 62 + 62 = 180

∴ m∠ ABD = 180 -124

∴ m∠ ABD = 56°     ................( 3 )

Now By angle addition property we have

m∠ ABC = m∠ ABD  + m∠ CBD

Substituting the values from equation 1 and equation 3 we get

∴ m∠ ABC = 56 + 60

∴ m∠ ABC = 116°

Therefore ,the measure of angle ABC = 116°.

4 0
3 years ago
Please answer all 3 questions
blsea [12.9K]

Answer:

  • x = 30°
  • DB = 26
  • AD = BC = AB = DC = 7

Step-by-step explanation:

  • <em>Diagonals of a square are congruent and perpendicular and bisect each other</em>
<h3>Q4</h3>

m∠AEB = 3x

m∠AEB = 90°

  • 3x = 90° ⇒ x = 30°
<h3>Q5</h3>

AE = 3x - 2

EC = 2x + 3

  • AE = EC
  • 3x - 2 = 2x + 3
  • 3x - 2x = 3 + 2
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DB = EC = 2(AE) = 2(3*5 - 2) = 2(13) = 26

<h3>Q6</h3>

<u>AD and BC are the sides, which are equal</u>

  • 2x - 1 = 5x - 13
  • 5x - 2x = 13 - 1
  • 3x = 12
  • x = 4

AD = BC = AB = DC =  2*4 - 1 = 7

7 0
2 years ago
Read 2 more answers
The sum of four consecutive even numbers is 60. Find the smallest of the four number.
Assoli18 [71]

Answer:

answer = 12

Step-by-step explanation:

Let the smallest number be x

So

X+(x+2)+(x+4)+(x+6)=60

4x+12=60

4x=48

X=12

7 0
2 years ago
vivian had to pay $22000 of student loans when he graduated. By the following year, his debt had been reduced to $ 15200. How mu
Andreas93 [3]

Answer:

He payed off 6,800$

Step-by-step explanation:

4 0
3 years ago
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