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3 years ago

Express the complex number in trigonometric form. -2 + 2 sqrt(3) i

Mathematics

2 answers:

KIM [24]3 years ago

6 0

Answer:

Step-by-step explanation:

Okay...

a+ib=r (costheta+isintheta)

r=sqrt a^2+b^2

r=sqrt (-2)^2+2 sqrt 3^2

r=4

theta= tan^-1 (y/x) or (b/a)

theta= tan^-1 (2 sqrt 3/-2)

theta=tan^-1(-sqrt 3)

theta=-60

180-60=120

(we know that theta is in the 2nd quadrant because ALL Students Take Calculus. All values are positive in quadrant one, Sin is positive in quadrant two, Tangent is positive in Quadrant three, and Cosine is positive in quadrant four. Since our y-value (sin) is positive it must occur in the 2nd quadrant. That is why I subtracted it from 180.

Convert degrees to radians: 120 times pi/180 =2pi/3

theta=2pi/3

So now we have our r value (4) and theta value (2pi/3). All we need to do now is substitute.

a+ib= 4(cos 2pi/3+isin2pi/3)

NARA [144]3 years ago

5 0

Hello,

-2+i*2√3=4(cos 120°+i sin 120°)

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What is the product of − 3/11 and − 2/15? please explain.

emmainna [20.7K]

ANSWER

The product is

$\frac{2}{55}$

EXPLANATION

To find the product of

$- \frac{3}{11}$

and

$\frac{ - 2}{15}$

means we should multiply the two fractions.

We multiply to obtain,

$- \frac{3}{11} \times - \frac{2}{15}$

$= - \frac{3}{11} \times - \frac{2}{3 \times 5}$

Cancel the common factors:

$= - \frac{1}{11} \times - \frac{2}{5}$

Now, multiply the numerators separately and the denominators too separately.

$= \frac{ - 1 \times - 2}{11 \times 5}$

This simplifies to,

$= \frac{2}{55}$

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3 years ago

In an election, 471 people voted. Candidate B received 2/3 of the votes. How many votes did Candidate B receive?

Vlada [557]

Answer:314

Step-by-step explanation:

314 votes

471 x (2/3) = 314

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3 years ago

Find the value of each variable in the circle to the right. The dot represents the center of the circle.

MrMuchimi

9514 1404 393

Answer:

a = 57.5

b = 90

c = 65

Step-by-step explanation:

The measure of an inscribed angle is half that of the arc it intercepts. The angle at 'a' intercepts an arc of 115°, so its measure is (115/2)° = 57.5°

The inscribed angle at 'b' is a semicircle, 180°, so the measure of 'b' is (180/2)° = 90°.

The arc 'c' is the remainder of a semicircle after 115° have been taken away. Its measure is 180° -115° = 65°.

(a, b, c) = (57.5, 90, 65)

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3 years ago

Help me!!! the question is in the attachment

pentagon [3]

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therefore the integers it's between are 16 and 17

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3 years ago

Suppose a triangle has sides a,b,and c and that a^2 + b^2

bagirrra123 [75]

Answer:

a^2+b^2=c^2

Step-by-step explanation:

a, b, c each represent a side. Lets say a triangle has a=2 and b=4.

a^2= 2^2= 2*2= 4 do the same with B.

b^2= 4^2= 4*4= 16

2. a^2+ b^2= 4+16= 20= c^2

8 0

4 years ago