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Softa [21]
3 years ago
15

Express the complex number in trigonometric form. 2 - 2i

Mathematics
2 answers:
LekaFEV [45]3 years ago
8 0
Trigonometric form of the complex number :  z = 2 - 2 i :
z = r ( cos t + i sin t )
r = | z | = √ ( 2² + (-2)² ) = √(4+4) = √8 = 2√2
t ( theta ) = tan^(-1) (-2 / 2 )= tan^(-1) (- 1 ) = - π / 4
z = 2√2 · ( cos (-π/4) + i sin (-π/4) ) =
= 2√2 · (  cos π/4  - i sin π/4 )
JulijaS [17]3 years ago
5 0

Answer:

a+ib=2sqrt2(cos7pi/4+isin7pi/4)

Step-by-step explanation:

a+ib=r (cos theta+isin theta)

r=sqrt a^2+b^2

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

r=2sqrt 2

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

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

theta=-45 degrees

Now, I know that theta is in the fourth quadrant because cos (x-value) is positive. So, I am going to subtract my value from 360 degrees.

360-45= 315

theta=315

I can convert degrees to radians (if need be): 315 times pi/180= 7pi/4

Theta=7pi/4 r=2sqrt2

Substitute: a+ib=2sqrt2(cos7pi/4+isin7pi/4)       this is radian format

or... a+ib=2sqrt2(cos 315+isin315)                       this is degree format

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anastassius [24]

Answer:

C

Step-by-step explanation:

A "zero" of a function is an input value that makes the function value equal zero.  On the graph these input values are -3 and 1; you can see that the function values are zero in both cases.  C is correct.

7 0
2 years ago
Witch mixed number shows the result of 89 divided by<br> 35
KATRIN_1 [288]

Answer:

89/35 = 2 and 19/35

Step-by-step explanation:

7 0
3 years ago
It is now quarter to ten. What time will it be in four hours and fifty-one minutes?
Veseljchak [2.6K]

Answer:it would be 2:22

Step-by-step explanation:

If there’s 25 minutes till 10 so therefore it would be 9:35 and since it’s 9:35 four hours and 51 minutes from then would be 2:22 because the minutes would add up to 82 minutes and four hours so your answers to 2:22

7 0
2 years ago
What is the volume of the prism?
mezya [45]

Answer:

40 \frac{5}{8} cm^{3}

Step-by-step explanation:

The figure is a rectangular prism, so the formula would be Volume = length x width x height.

length =  6 \frac{1}{2} cm

width  =  2 \frac{1}{2} cm

height  =  2 \frac{1}{2} cm

If you plug everything you have in the problem into the volume equation, you would get : Volume = 6 \frac{1}{2} cm x 2 \frac{1}{2} cm x 2 \frac{1}{2} cm.

Without a calculator, I would first turn the mixed numbers into improper fractions.

  • 6 \frac{1}{2}  = \frac{13}{2}
  • 2 \frac{1}{2} = \frac{5}{2}

Volume = \frac{13}{2} x  \frac{5}{2} x  \frac{5}{2}

When you multiply everything together you should get \frac{325}{8}.

As a mixed number, that would be 40 \frac{5}{8} cm^{3}.

7 0
3 years ago
When creating a histogram, the first recorded scale is 0 to 10. What should the second scale indicate?
klio [65]

Answer:

A) 10-20

Step-by-step explanation:

Its A because it started with 0 and it went to 10 so it adds 10 each time cause it gave us the hint with 0 to 10,

I hope this helps

6 0
2 years ago
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