1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
KATRIN_1 [288]
2 years ago
15

Let z = 0.3(cos(31°) + i sin(31°)) and w = 20(cos(18°) + i sin(18°)).

Mathematics
2 answers:
babunello [35]2 years ago
5 0

Answer:

c. Stretch z by a factor of 20, then rotate 18° counterclockwise.

Step-by-step explanation:

Yuliya22 [10]2 years ago
4 0

Answer:

Option (C) is correct.

Step-by-step explanation:

Given that z = 0.3(cos(31°) + i sin(31°)) and 20(cos(18°) + i sin(18°)).

The product of both the complex number is

zw = [0.3(cos(31°) + i sin(31°))] x [20(cos(18°) + i sin(18°))]

=(0.3x20)[cos(31°) x cos(18°) + cos(31°) x i sin(18°) + i sin(31°) x cos(31°)+ i sin(31°) x i sin(18°)]

Here, (0.3x20)=6, is the magnitude of zw, which is stretching of 0.3 by 20.

zw=6[cos(31°) x cos(18°) + i{cos(31°) x sin(18°) + sin(31°) x cos(31°)}+ i² sin(31°)x sin(18°)]

As i²= -1, So

zw=6[cos(31°) x cos(18°) + i{cos(31°) x sin(18°) + sin(31°) x cos(31°)} - sin(31°)x sin(18°)]

=6[{cos(31°) x cos(18°)- sin(31°)x sin(18°)} + i{cos(31°) x sin(18°) + sin(31°) x cos(31°)}]

As cosAcosB - sin A sin B = cos (A+B) and cosAsinB + sin A sos B = sin (A+B), so

zw=6[cos(31°+18°) + i{sin(31°+18°)]

Note that, initially the argument of z is 31° and after rotation of 18° in counterclockwise direction, the argument od zw is 31°+18°= 49°. i.e

zw=6(cos(49°) + isin(49°)).

So, zw can be determined by stretching z by a factor of 20, then rotating by 18° counterclockwise.

Hence, option (C) is correct.

You might be interested in
What is the equation of a circle whose center is (2,0) and has a radius= 9?
Flauer [41]
The equation of a circle is: (x - h)² + (y - k)² = radius² where (h, k) is the center. Now just plug in your given information and simplify.

(x - 2)² + (y - 0)² = 9²

Your equation is:
(x - 2)² + y² = 81
6 0
3 years ago
Read 2 more answers
Cal had $15. He spent $3 on pens and $8 on a book.
nikklg [1K]
He spent $11 dollars minus tax
3 0
3 years ago
Read 2 more answers
What is the degree of the polynomial given below?
Ivenika [448]

Answer:

it is 3 i am pretty sure

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
What is the y-coordinate of the point shown in the graph?
murzikaleks [220]

Answer:

3,-7

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
What is 0.2401 as a fraction
vlabodo [156]

Answer:

24/100 or 6/25

Step-by-step explanation:

.24 is the same as 24/100 if you need to simplify then just find a common number to divide by.


Hope this helps! Please mark Brainliest! Have a great day!



Thank you for using Brainly!

3 0
3 years ago
Read 2 more answers
Other questions:
  • A painter is painting a wall with an area of 150 ft2. He decides to paint half of the wall and then take a break. After his brea
    9·2 answers
  • Which correctly shows how to use the GCF and the distributive property to find an expression equivalent to 8 + 48?
    14·2 answers
  • Graph <br> f(x) = 3/2 + 2
    5·1 answer
  • PLEASEEEE HELPPPPP MEEEEEE!!!!<br> Find h in the diagrams below.
    15·1 answer
  • The sum of the first 3 terms of a geometric series is 171 and the common ratio is 2/3
    12·1 answer
  • Donald has x twenty dollar bills and one ten dollar bill how much money does Donald have
    7·2 answers
  • 4x-3y=-15 In slope form
    8·1 answer
  • A recipe includes 6 cups of flour and 3 cup of shortening. Write the ratio of the amount of flour to the amount of shortening as
    9·1 answer
  • By how many times does the surface area of a sphere differ if radius is double​
    13·2 answers
  • A rectangle has a length represented by the function f(x) and a width represented by g(x).
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!