Find the area of the shaded polygons:

The complex number -7i into trigonometric form is 7 (cos (90) + sin (90) i) and 3 + 3i in trigonometric form is 4.2426 (cos (45) + sin (45) i)

<h3>What is a complex number?</h3>

It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.

We have a complex number shown in the picture:

-7i(3 + 3i)

= -7i

In trigonometric form:

z = 7 (cos (90) + sin (90) i)

= 3 + 3i

z = 4.2426 (cos (45) + sin (45) i)

$\rm 7\:\left(cos\:\left(90\right)\:+\:sin\:\left(90\right)\:i\right)4.2426\:\left(cos\:\left(45\right)\:+\:sin\:\left(45\right)\:i\right)$

$\rm =7\left(\cos \left(\dfrac{\pi }{2}\right)+\sin \left(\dfrac{\pi }{2}\right)i\right)\cdot \:4.2426\left(\cos \left(\dfrac{\pi }{4}\right)+\sin \left(\dfrac{\pi }{4}\right)i\right)$

$\rm 7\cdot \dfrac{21213}{5000}e^{i\dfrac{\pi }{2}}e^{i\dfrac{\pi }{4}}$

$\rm =\dfrac{148491\left(-1\right)^{\dfrac{3}{4}}}{5000}$

=21-21i

After converting into the exponential form:

$\rm =\dfrac{148491\left(-1\right)^{\dfrac{3}{4}}}{5000}$

From part (b) and part (c) both results are the same.

Thus, the complex number -7i into trigonometric form is 7 (cos (90) + sin (90) i) and 3 + 3i in trigonometric form is 4.2426 (cos (45) + sin (45) i)

Learn more about the complex number here:

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3 0

2 years ago

Paula purchase 3 dvd and 7 cds and spent between 90 and 100. Each dvd costs the same amount the price of cd is 10 select all amo

sveticcg [70]

The options aren't given, however, the range of amount spent could be calculated

Answer:

Kindly check explanation

Step-by-step explanation:

Paula purchase 3 dvd and 7 cds and spent between 90 and 100. Each dvd costs the same amount the price of cd is 10 select all amounts that could be the price of the dvd

Given that :

DVD costs the same amount

Number of DVD's = 3

Cost of cds = 10

Number of cds = 7

Total cost of cd's = 10 * 7 = 70

Let the price of DVD = x

Total amount spent = 90 - 100

Lowest price of DVD :

(amount spent - price of cd) / number of dvd

(90 - 70) / 3 = 20 /3 = 6.667

Highest price :

(100 - 70) / 3 = 30 / 3 = 10

Hence the pice of each DVD will range between /

6.6666 and 10.

Hence, prices listed within the range above are possible.

3 0

2 years ago

Sara bought 36 ounces of cheese for 3.24 what was the unit price of cheese

slava [35]

Answer:

$0.09

Step-by-step explanation:

Unit price= total price/ total units

$3.24/ 36oz= $0.09

3 0

3 years ago

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