Ask question

Ask question

All categories

3 years ago

8

Find the product of the complex numbers. Express your answer in trigonometric form.

1 answer:

alekssr [168]3 years ago

4 0

<span>10(cos(4pi/3) + i sin(4pi/3)) To multiply complex numbers in trigonometric form, you simply multiply the radii and add the thetas. We have: z1=5(cos(pi/2)+i sin(pi/2)) z2=2(cos(5pi/6)+i sin(5pi/6)) The radii for the above 2 numbers are 5 and 2. So the result will have a radius of 5*2 = 10. The thetas are pi/2 and 5pi/6, so the new theta will be pi/2 + 5pi/6 = 3pi/6 + 5pi/6 = 8pi/6 = 4pi/3. So the answer is: 10(cos(4pi/3) + i sin(4pi/3))</span>

You might be interested in

This is my last question please help me

anastassius [24]

Answer:

Angle ADC = 80 degrees

Step-by-step explanation:

Here, we want to find the measure of angle ADC

mathematically, sum of angles at a point is 360

Thus;

x + 3x + x + 10 = 360

5x + 10 = 360

5x = 360-10

5x = 350

x = 350/5

x = 70

From the diagram;

angle ADC is (x + 10)

so we have; (70 + 10) = 80 degrees

7 0

3 years ago

PLEASE HELP!! NO LINKS!! GIVING 20 POINTS AWAY!!

shutvik [7]

Answer:

$m\angle N = 32\degree$

$m\widehat {NQ}=106\degree$

Step-by-step explanation:

By inscribed angle theorem:

$m\angle N = \frac{1}{2} \times m\widehat {MP}$

$m\angle N = \frac{1}{2} \times 64\degree$

$m\angle N = 32\degree$

Again by inscribed angle theorem:

$m\angle P= \frac{1}{2} \times m\widehat {NQ}$

$53\degree = \frac{1}{2} \times m\widehat {NQ}$

$2\times 53\degree = m\widehat {NQ}$

$m\widehat {NQ}=106\degree$

5 0

3 years ago

A rectangle's length, x, is 2 meters greater than its width. If the perimeter of the rectangle is greater than 112 meters, what

kotykmax [81]

Assume widthis x-2
perimeter is 2*(width+length)
so 2*(x+x-1)>112
2*(2x-1)>112
4x-2>112
x>28.5
so any length greater than 28.5 will work

6 0

4 years ago

The<br> of -6 is 6, because it is 6 units from zero on<br> the number line.

Greeley [361]

Answer:

not answerable

Step-by-step explanation:

7 0

3 years ago

Find the surface area of the figure below

Vera_Pavlovna [14]

Answer:

310.8m²

Step-by-step explanation:

<u>GIVEN :-</u>

Diameter = 9m ⇒ Radius (r) = 9/2 = 4.5m
Slant height (l) = 13m

<u>TO FIND :-</u>

Surface area of the whole figure.

<u>FORMULAES TO KNOW BEFORE SOLVING :-</u>

Curved surface area of cone = $\pi rl$ (where r = radius & l = slant height)
Curved surface area of hemisphere = $2\pi r^2$ (where r = radius)

<u>PROCEDURE :-</u>

In the figure , the cone is mounted on a hemisphere.

⇒ Radius of cone = Radius of hemisphere = 4.5m

Total surface area of the figure = Curved surface area of both cone & hemisphere.

⇒

Curved surface area of cone = $\pi rl = 3.14 \times 4.5 \times 13 = 183.69m^2$ ≈ 183.7m²

Curved surface area of hemisphere = $2\pi r^2 = 2 \times 3.14 \times (4.5)^2 = 127.17m^2$ ≈ 127.1m²

∴ Total surface area = 183.7 + 127.1 = 310.8m²

4 0

3 years ago