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jek_recluse [69]
3 years ago
13

Find the product of z1 and z2, where z1 = 2(cos 70° + i sin 70°) and z2 = 4(cos 200° + i sin 200°)

Mathematics
2 answers:
Scilla [17]3 years ago
6 0

Answer: <u>-8i</u>

2(cos 70 + i sin 70) * 4(cos 200 +isin 200)

8 (cos (70+200) + i sin (70+200)     factor a i sin 70 out

8 (cos(270) + i sin (270))

cos 270 is (0,-1)   sin 270 is -1 from the unit circle

cos 270 is 0

8 (0 -i)

<u>-8i</u>

vazorg [7]3 years ago
5 0

Answer:

-8i

Step-by-step explanation:

To multiply numbers is polar form

z1 = r1 ( cos theta 1 + i sin theta 1)

z2 = r2 ( cos theta 2 + i sin theta 2)

z1*z2 = r1*r2 (cos (theta1+theta2) + i sin (theta1+theta2)

z1 = 2(cos 70° + i sin 70°)

z2 = 4(cos 200+ i sin 200)

z1z2 = 2*4 (cos (70+200) + i sin (70+200)

z1z2 = 8 (cos(270) + i sin (270))

       = 8 (0 + i (-1))

       =-8i

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Answer:

49º

Step-by-step explanation:

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3 years ago
The rate of change of y with respect to t is proportional to 50 - y
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3 0
3 years ago
Which function is the same as y=cos(2(x+pi/2))-2
miss Akunina [59]
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8 0
3 years ago
Write y = x2 + 24x + 144 as a square of binomial.
irina1246 [14]

Answer:

y=(x+12)^2\\

Step-by-step explanation:

To write a quadratic equation into binomial form we can compare the equation into the completing square form of a quadratic equation like this ,

y=a(x-h)^2+k

now since,

y=x^2+24x+144

we can equate both the equations from left hand side to right hand side like this,

x^2+24x+144=a(x-h)^2+k\\

now we solve,

x^2+24x+144=a(x-h)^2+k\\x^2+24x+144=a((x)^2-2(x)(h)+(h)^2)+k\\x^2+24x+144=a(x^2-2hx+h^2)+k\\x^2+24x+144=ax^2-2ahx+ah^2+k\\

now we compare the coefficients of x^2:

1 = a\\

now we compare the coefficients of x :

24=-2ah\\24=-2(1)h\\24=-2h\\\frac{24}{-2}=h\\-12=h\\

now we compare the constants , (constants are the letters which are not associated with any variable in this case the variable is x)

144 = ah^2+k\\144=(1)(-12)^2+k\\144=(1)(144)+k\\144=144+k\\144-144=k\\0=k\\

so now the value we got all the values for the completing square form we plug those in , a = 1 , h = -12 , k = 0 ,

y=a(x-h)^2+k\\y=1(x-(-12))^2+0\\y=(x+12)^2\\

this is the square of a binomial, if you want to verify if we expands this formula by the formula of (a + b)^2 we would get the same result. Thus this is the correct answer.

5 0
3 years ago
HELP NEED AN ANSWER DUE TODAY!!
AnnyKZ [126]

z < 1.25

I used mathaway it's correct

4 0
3 years ago
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