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
Is this equation an identity?<br><br> z = -10 − z
Umnica [9.8K]

Answer:

y

Step-by-step explanation:

3 0
2 years ago
8 to 11 do it with equations thx
Alenkasestr [34]

Answer:

Step-by-step explanation:

8. 4\geq x+\frac{3}{4}

4(4\geq x+\frac{3}{4} )

16\geq 4x + 3

-3         -3

13\geq 4x

\frac{13}{4}\geq \frac{4x}{4}

\frac{13}{4} \geq x = x\leq \frac{13}{4}

x\leq \frac{13}{4}=3.25

9. x-3\leq -8

       +3     +3

x\leq -5}

10. 4\leq x-7

  +7         +7

11\leq x=x\geq 11

11. 6.9 < x - 2.3

 + 2.3      + 2.3

 9.2 < x = x > 9.2

Hope this helps!

5 0
2 years ago
Pls help Im very stuck on this and don’t understand
Lady bird [3.3K]

Answer:

C. 85 degrees

Step-by-step explanation:

Step 1: Set up equation

x + 57 + 96 + x = 131

Step 2: Solve for <em>x</em>

2x + 153 = 131

2x = -22

x = -11

Step 3: Find m∠RQU

m∠RQU = 96 + <em>x</em>

m∠RQU = 96 - 11

m∠RQU = 85°

8 0
3 years ago
Help me Please I'm confused!!!!!!!
Andrew [12]

Answer:

5 x k = 15 + 3 = 18

Step-by-step explanation:

k=3

6 0
3 years ago
Collin's retirement party costs $4 for every guest he invites. What is the maximum number of guests there can be if Collin can a
steposvetlana [31]

Answer:

Collin can invite maximum 6 guest to his retirement party.

Step-by-step explanation:

Total cost of retirement party = $24

Cost to be spend on each guest = $4

Number of guests to be invited in the retirement party= x

x\times \$4=\$24

x=\frac{\$24}{\$4}

x = 6

Collin can invite maximum 6 guest to his retirement party.

6 0
3 years ago
Other questions:
  • Can anyone help me with this problem?
    8·1 answer
  • What is the sum? (3/x2-9) + (5/x+3)
    12·2 answers
  • A cell phone service provider offers two plans. Plan A includes a fee of $25 per month and charges $0.25 for every call. Plan B
    12·1 answer
  • AB contains the points A(–3, 3) and B(1, 4). YZ contains the points Y(–4, 7) and Z(–2, y). AB and YZ are perpendicular. Find the
    13·2 answers
  • What is a similarity between the empirical rule and​ chebychev's theorem?
    13·1 answer
  • After 10 years, Hamid's account earned $300 in interest. If the interest rate (in decimal form) is 0.06, how much did Hamid init
    6·1 answer
  • SOMEONE PLS HELP IM CONFUSED , WILL MARK BRAINLIEST
    8·1 answer
  • Please help I will give brainliest
    15·1 answer
  • Write the following as an expression: How much water do I need to add to l liters of pure alcohol to obtain a solution of 45% al
    12·1 answer
  • Hey can anyone help me find the missing side lengths please and thank you
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!