Need help with complex numbers question. Watch

Adil2400
Badges: 7
Rep:
?
#1
Report Thread starter 4 weeks ago
#1
Find in exponential form (2+2i)^(4/3). There’s meant to be more than one answer. Please show working out so I understand it.
0
reply
RDKGames
  • Community Assistant
Badges: 20
Rep:
?
#2
Report 4 weeks ago
#2
(Original post by Adil2400)
Find in exponential form (2+2i)^(4/3). There’s meant to be more than one answer. Please show working out so I understand it.
Convert 2+2i into exponential form first.
0
reply
hcaushi
Badges: 14
Rep:
?
#3
Report 4 weeks ago
#3
First thoughts: Let z=a+bi. Let z^3 = (2+2i)^4. To work this out, you can use the modulus and argument of each of them, and find out which arguments equate.
0
reply
Adil2400
Badges: 7
Rep:
?
#4
Report Thread starter 4 weeks ago
#4
(Original post by RDKGames)
Convert 2+2i into exponential form first.
I can do that but how many answers are there supposed to be? If we were working out (2+2i)^(1/3), there would be 3 answers. How many answers are there for (2+2i)^(4/3)?
0
reply
RDKGames
  • Community Assistant
Badges: 20
Rep:
?
#5
Report 4 weeks ago
#5
(Original post by Adil2400)
I can do that but how many answers are there supposed to be? If we were working out (2+2i)^(1/3), there would be 3 answers. How many answers are there for (2+2i)^(4/3)?
Still three, because of the cube root.
0
reply
Adil2400
Badges: 7
Rep:
?
#6
Report Thread starter 4 weeks ago
#6
(Original post by RDKGames)
Still three, because of the cube root.
How do you know there’s not 4 because of the power of 4?
0
reply
RDKGames
  • Community Assistant
Badges: 20
Rep:
?
#7
Report 4 weeks ago
#7
(Original post by Adil2400)
How do you know there’s not 4 because of the power of 4?
Because you're not taking a fourth root...

At the end of the day nth root means we are solving some equation z^n = ... and by Fundamental Theorem of Algebra we know this has n roots.
0
reply
Adil2400
Badges: 7
Rep:
?
#8
Report Thread starter 4 weeks ago
#8
(Original post by RDKGames)
Because you're not taking a fourth root...

At the end of the day nth root means we are solving some equation z^n = ... and by Fundamental Theorem of Algebra we know this has n roots.
ok thanks. If you can, please attempt the question and tell me what you get. I want to see if I get the same answers.
0
reply
RDKGames
  • Community Assistant
Badges: 20
Rep:
?
#9
Report 4 weeks ago
#9
(Original post by Adil2400)
ok thanks. If you can, please attempt the question and tell me what you get. I want to see if I get the same answers.
Easier if you post your answers here and I just look at them tbh
0
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

University open days

  • University of Roehampton
    Department of Media, Culture and Language; School of Education; Business School Undergraduate
    Tue, 19 Feb '19
  • Edge Hill University
    Undergraduate and Postgraduate - Campus Tour Undergraduate
    Tue, 19 Feb '19
  • University of Kent
    Sciences, Social Sciences and Humanities Further education
    Tue, 19 Feb '19

Do you give blood?

Yes (61)
8.29%
I used to but I don't now (18)
2.45%
No, but I want to start (275)
37.36%
No, I am unable to (177)
24.05%
No, I chose not to (205)
27.85%

Watched Threads

View All
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise