Welcome :: Homework Help and Answers :: Mathskey.com
Welcome to Mathskey.com Question & Answers Community. Ask any math/science homework question and receive answers from other members of the community.

13,435 questions

17,804 answers

1,438 comments

774,905 users

When a complex number is in trigonometric form

0 votes
When a complex number is in trigonometric form r times the quantity of cosine of theta + i times sine of theta.
what does theta represent? 
A. abscissa
B. argument
C. imaginary unit
D. modulus
 
Find Bracket. 5 times the quantity of cosine of 20 degrees + i times sine of 20 degrees. bracket. to the third power. and write the answer in standard form. 
A. image
B. image
C. image
D. image
Find 2 times the quantity of the square root of 3 + i where the quantity is taken to the seventh power. and write the answer in standard form. 
A. image
B. image
C. image
D. image

 

closed with the note: fghgjhkhj
asked Oct 16, 2014 in TRIGONOMETRY by tonymate Pupil
closed Oct 17, 2014 by tonymate

3 Answers

0 votes
 
Best answer

1)

The complex number

z = r(cos θ + i sin θ)

θ represents argument of the complex number .

Option B is correct.

answered Oct 16, 2014 by bradely Mentor
selected Oct 17, 2014 by tonymate
0 votes

 [ 5 (cos20° + i sin20°)]³

Using De Moivre’s theorem:

If z =  r(cos θ + i sin θ) then zn = [r(cos θ + i sin θ)]n =[rn(cos nθ + i sin nθ)]

[ 5 (cos20° + i sin20°)]³ = 5³(cos 3(20°) + i sin3(20°))

                                               =125(cos 6 + i sin6)

                                               =125[(1/2) + i (√3/2)]

                                                =125[(1/2) + i (√3/2)]

                                     =(125/2) + i 125(√3/2)

Option C is correct.

answered Oct 16, 2014 by bradely Mentor
0 votes

2 (√3 + i)7

Convert the √3 + i to polar form:

Find the magnitude of the complex number.

r = √[(√3)² +(1)²]

   = √[3 +1]

   = 2

Find the argument of the complex number.

θ = tan-1 (1/√3) = 30°

√3 + i = 2 (cos30° + i sin30°)

Using De Moivre’s theorem:

If z =  r(cos θ + i sin θ) then zn = [r(cos θ + i sin θ)]n =[rn(cos nθ + i sin nθ)]

2 (√3 + i)7 = 2[2 (cos30° + i sin30°)]7

                     = 2(2)7(cos 7(30°) + i sin7(30°))

                =(2)8(cos 210° + i sin210°)

                 =(2)8(cos (180°+30°) + i sin(180°+30°))

                      =(2)8(- cos 30° - i sin 30°)

                      =256(- (√3/2) - i (1/2))

                 =-128√3 -128 i

Option D is correct.

answered Oct 16, 2014 by bradely Mentor

Related questions

...