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oksian1 [2.3K]
2 years ago
10

Find the trigonometric form of the number 3 + √3i.

Mathematics
1 answer:
sattari [20]2 years ago
3 0

Any complex number z can be written in trigonometric form as

z = |z| e^{i\arg(z)} = |z| \left(\cos(\arg(z)) + i \sin(\arg(z))\right)

where |z| is the modulus of z and \arg(z) is its argument, i.e. the angle z makes with the positive real axis in the complex plane.

We have

|z| = \sqrt{3^2 + \left(\sqrt3\right)^2} = \sqrt{12} = 2\sqrt3

and

\arg(z) = \tan^{-1}\left(\dfrac{\sqrt3}3\right) = \tan^{-1}\left(\dfrac1{\sqrt3}\right) = \dfrac\pi6

Then

3 + \sqrt3 \, i = \boxed{2\sqrt 3 \left(\cos\left(\dfrac\pi6\right) + i \sin\left(\dfrac\pi6\right)\right)}

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Two pupils each drew a triangle with one side of 6 cm , one side of 10 cm and one side of 7 cm. Must their triangles be congruen
7nadin3 [17]

Answer:

no

Step-by-step explanation:

they can be either side because the numbers are different in the angles

5 0
3 years ago
Factor Trinomials:
notka56 [123]

Answer:

1. 2(x+2)(x+5)

2. 8(x+4)^{2}

Step-by-step explanation:

<u>Problem #1:</u>

1. Find the GCF (Greatest Common Factor)

GCF = 2

2. Factor out the GCF and simplify.

2(x^{2} +7x+10)

3. Factor x^{2} +7x+10

<u>Which two numbers add up to 7 and multiply to 10?</u>

2 and 5

<u>Rewrite the expression using the above.</u>

(x+2)(x+5)

4. Done!

2(x+2)(x+5)

<u>Problem #2:</u>

1. Find the GCF (Greatest Common Factor)

GCF=8

2. Factor out the GCF and simplify.

8(x^{2} +8x+16)

3. Use the perfect square formula. a^{2} +2ab+b^{2} =(a+b)^{2}

a = x\\b=4

(x+4)^{2}

4. Done!

8(x+4)^{2}

8 0
2 years ago
Given the trigonometric function value of theata Find the exact value of all remaining trigonometric function csc(theata)= 7
Monica [59]
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8 0
2 years ago
What is the value of x in the equation 3-2x--15x?<br><br> 6<br> 2<br> 2<br> 6
Wittaler [7]

Consider the given equation is 3-2x=15 and one of the 6 in the options is -6.

Given:

The equation is

3-2x=15

To find:

The value of x.

Solution:

We have,

3-2x=15

Subtracting 3 from both sides, we get

3-2x-3=15-3

-2x=12

Divide both sides by -2.

x=\dfrac{12}{-2}

x=-6

Therefore, the value of x is -6.

6 0
3 years ago
How would the graph of the relation y=3x-2 change if the 3 and -2 were both doubled? 
Lena [83]
<u>y = 3x - 2</u>

-- The ' 3 ' is the slope. If you double it to ' 6 ', the line is steeper.

-- The ' -2 ' is the y-intercept. If you double it to ' -4 ', the line crosses the y-axis lower.

Choice <u>(a)</u> says that . . . "... steeper, and lower y-intercept".

6 0
3 years ago
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