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3 years ago

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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2 years ago

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Answer:

Mr. Dairo can produce 20580 pieces of Papaya rosette in two weeks.

Step-by-step explanation:

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$a_1 = 5890\\a_2 = 7020\\a_3 = 8150$

We can check if these numbers are part of a sequence.

In order to check, common difference will be found first.

$d = a_2-a_1 = 7020-5890 = 1130\\d =a_3-a_2 = 8150-7020 = 1130$

It can be observed that the common difference is same. When the common difference is same, the sequence is said to be an arithmetic sequence.

The formula for arithmetic sequence is given by:

$a_n = a_1+(n-1)d$

Putting the values

$a_n = 5890+(n-1)(1130)\\a_n = 5890+1130n-1130\\a_n =4760+1130n$

The formula for nth term can be used to find any term. As we have to find the number of papaya rosette pieces after two weeks which means that we need to find the number of pieces on 14th day.

So,

$a_{14}= 4760+1130(14)\\a_{14} = 4760+15820\\a_{14} = 20580$

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Mr. Dairo can produce 20580 pieces of Papaya rosette in two weeks.

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2 years ago

The amount of money in a savings account after t years is represented by the function f(t)=3600(1.035)t .

timama [110]

Answer: The initial amount in the account = $3600

Step-by-step explanation:

Since we have given that

The amount of money in a savings account after t years is represented by the function

$f(t)=3600(1.035)^t$

As we know the formula "Compound Interest" :

$Amount=P(1+\frac{r}{100})^t\\\\Here,\\\\\text{ P denotes principal}\\\\\text{ R denotes Rate of interest}\\\\\text{ T denotes time}$

So, According to our question,

Rate of interest = 0.35 = 35%

So, equate the both the equations , we get that

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3 years ago

Read 2 more answers

NEED HELP ASAP!!!!!!!

sertanlavr [38]

ANSWER: x > -6
1. subtract 12 from each side
2. divide by -3 which will make the sign flip

8 0

3 years ago

(x+16)²=12 plz help me and show work

Readme [11.4K]

Answer:

The answer is $x=-16$ ± $2\sqrt{3}$ in exact form or $x=-12.535898$ , $x=-19.464102$ in decimal form.

Step-by-step explanation:

To solve this problem, start by moving all terms to the left side of the equation and simplify. Simplify the equation by subtracting 12 from both sides of the equation and squaring $x+16$ , which will look like $x^{2} +32x+256-12=0$ . Next, simplify the equation again, which will look like $x^{2} +32x+244=0$ .

Then, use the quadratic formula to find the solutions. The quadratic formula looks like $\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}$ .

For this problem, the quadratic variables are as follows:

$a=1$

$b=32$

$c=244$

The next step is to substitute the values $a=1$ , $b=32$ , and $c=244$ into the quadratic formula and solve. The quadratic formula will look like $\frac{-32(+-)\sqrt{32^2-4(1*244)} }{2*1}$ . To simplify the equation, start by simplifying the numerator, which will look like $x=\frac{-32(+-)4\sqrt{3} }{2*1}$ . Then, multiply 2 by 1 and simplify the equation, which will look like $x=-16(+-)2\sqrt{3}$ . The final answer is $x=-16$ ± $2\sqrt{3}$ in exact form. In decimal form, the final answer is $x=-12.535898$ , $x=-19.464102$ .

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2 years ago