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
Ainat [17]
3 years ago
11

What are the fourth roots of 6+6√(3i) ?

Mathematics
1 answer:
Helen [10]3 years ago
8 0

Answer:

Step-by-step explanation:

The genral form of a complex number in rectangular plane is expressed as z = x+iy

In polar coordinate, z =rcos ∅+irsin∅ where;

r is the modulus = √x²+y²

∅ is teh argument = arctan y/x

Given thr complex number z = 6+6√(3)i

r = √6²+(6√3)²

r = √36+108

r = √144

r = 12

∅ = arctan 6√3/6

∅ = arctan √3

∅ = 60°

In polar form, z = 12(cos60°+isin60°)

z = 12(cosπ/3+isinπ/3)

To get the fourth root of the equation, we will use the de moivres theorem; zⁿ = rⁿ(cosn∅+isinn∅)

z^1/4  = 12^1/4(cosπ/12+isinπ/12)

When n = 1;

z1 =  12^1/4(cosπ/3+isinn/3)

z1 = 12^1/4cis(π/3)

when n = 2;

z2 = 12^1/4(cos2π/3+isin2π/3)

z2 = 12^1/4cis(2π/3)

when n = 3;

z2 = 12^1/4(cosπ+isinπ)

z2 = 12^1/4cis(π)

when n = 4;

z2 = 12^1/4(cos4π/3+isin4π/3)

z2 = 12^1/4cis(4π/3)

You might be interested in
A van travels 150 miles on 6 gallons of gas. How many gallons will it need to travel 325 miles?
diamong [38]

Answer:

C. 13 gallons

Step-by-step explanation:

150 divided by 6 is 25. 325 divided by 25 is 13.

8 0
3 years ago
What is the volume of the cube if the side length is 40cm​
swat32

Answer:

The formula to find the volume of a cube : s^3 so

S=40 cm

Now

by the formula,

40^3

64000

7 0
2 years ago
a salesperson earns 9 commission on sales.the equation for the amount he or she earns in commission is c = 0.9s, where s is the
NNADVOKAT [17]

Answer:

c = $5,400

Step-by-step explanation:

Given:

c = 0.9s

where,

s = amount sold

c = commission on sales

How much commission will he or she earn if the amount sold is $6,000?

Find c when she = $6,000

c = 0.9s

= 0.9 × 6,000

= 5,400

c = $5,400

(c, s) (5400, 6000)

3 0
3 years ago
What is equivalent to 35d-25
baherus [9]

Answer:

5(7d-5)

Step-by-step explanation:

taking 5 common from  35d-25

= 5(7d- 5)

7 0
3 years ago
Read 2 more answers
Find the GFC of 56 and 84. A factor tree for 84 is given below. The GCF of 84 and 56 is 7142128 .
guajiro [1.7K]

Answer:

28 is the GCF

Step-by-step explanation:

What I know about GCF is that it's a greatest (G) common (C) factor (F). The GCF of 84 and 56 is 7142128; false.

56- 56, 28, 14, 8, 7, 4, 2, 1.

84- 84, 42, 28, 21, 14, 12, 7, 6, 4, 3, 2, 1.

Hope this helps. :)

8 0
3 years ago
Read 2 more answers
Other questions:
  • MATH HELP???
    15·1 answer
  • For all real numbers a and b, 2a • b = a2 + b2<br> True or False? explain please
    15·1 answer
  • Solve the inequality. Enter the answer as an inequality that shows the value of the variable; for example f &gt; 7, or 6 &lt; w.
    6·1 answer
  • Which of the following are In The correct order from least to greatest?
    11·1 answer
  • 3^2(3^3)^2.3^-8 simplify
    10·1 answer
  • Find the new number given the Original number and the percent of change
    14·2 answers
  • PLEASE HELP !!!!The sum of three consecutive even integers is -36. Find the integers.(just show that the integers sum to -36)
    12·2 answers
  • Combine like terms 3x + 2x + 3y - 7y
    7·2 answers
  • What is the value of y in this diagram?<br> A. 61<br> B. 58<br> C. 21<br> D. 138
    5·1 answer
  • Detailed explanation please! (will give Brainliest)
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!