- Forums
###### complex numbers confusion

Watch

1 year ago

So I've been trying to practice evaluating complex numbers raised to an integer power. Here's an example problem from a sheet that I followed and its solution:

https://cdn.discordapp.com/attachments/692344148212187226/1004881882187579413/Screenshot_39.png

However when I tried to evaluate (-1 + i)^7 using the same procedure from the solution above I got the wrong answer and the solution for it incorporated costheta + isintheta whereas the example from above didn't. Is there a problem with the example that I followed or have I done something wrong?

The video linked has the full solution to (-1 + i)^7:

https://youtu.be/hoOJb5oqSSk

Here's my full working (again imitating the steps used in the solution from the sheet):

https://media.discordapp.net/attachments/692344148212187226/1005077869313142804/20220805_123915.jpg?width=927&height=473

https://cdn.discordapp.com/attachments/692344148212187226/1004881882187579413/Screenshot_39.png

However when I tried to evaluate (-1 + i)^7 using the same procedure from the solution above I got the wrong answer and the solution for it incorporated costheta + isintheta whereas the example from above didn't. Is there a problem with the example that I followed or have I done something wrong?

The video linked has the full solution to (-1 + i)^7:

https://youtu.be/hoOJb5oqSSk

Here's my full working (again imitating the steps used in the solution from the sheet):

https://media.discordapp.net/attachments/692344148212187226/1005077869313142804/20220805_123915.jpg?width=927&height=473

Reply 1

1 year ago

This is year 2 Further Maths.

21pi/4 = -3pi/4. This means your final answer should be 8root2 e^(-3pi/4), in exponential form, since 2^7/2 = 2^3 x 2^1/2 = 8root2. This is equivalent to -8 - 8i.

21pi/4 = -3pi/4. This means your final answer should be 8root2 e^(-3pi/4), in exponential form, since 2^7/2 = 2^3 x 2^1/2 = 8root2. This is equivalent to -8 - 8i.

Reply 2

1 year ago

Original post by Driving_Mad

This is year 2 Further Maths.

21pi/4 = -3pi/4. This means your final answer should be 8root2 e^(-3pi/4), in exponential form, since 2^7/2 = 2^3 x 2^1/2 = 8root2. This is equivalent to -8 - 8i.

21pi/4 = -3pi/4. This means your final answer should be 8root2 e^(-3pi/4), in exponential form, since 2^7/2 = 2^3 x 2^1/2 = 8root2. This is equivalent to -8 - 8i.

Ah I see, so the method from the sheet gets you directly to the modulus of the final complex number. Also where did the negative in front of 3pi/4 come from and why was 21pi/4 divided by 7?

Original post by Driving_Mad

This is year 2 Further Maths.

21pi/4 = -3pi/4. This means your final answer should be 8root2 e^(-3pi/4), in exponential form, since 2^7/2 = 2^3 x 2^1/2 = 8root2. This is equivalent to -8 - 8i.

21pi/4 = -3pi/4. This means your final answer should be 8root2 e^(-3pi/4), in exponential form, since 2^7/2 = 2^3 x 2^1/2 = 8root2. This is equivalent to -8 - 8i.

I presume you're working mod 2pi. What you've written isn't exactly right, is it?

Reply 4

1 year ago

Original post by davros

I presume you're working mod 2pi. What you've written isn't exactly right, is it?

could you elaborate please?

Reply 5

1 year ago

Original post by Soul Wavel3ngth

could you elaborate please?

Think of an Argand diagram. The real axis starts at argument 0. You go 2pi radians around you end up in the same position you started in. Going around 2pi again gives an argument of 4pi which ends up at the positive real axis again, so 0 is equivalent to 2kpi (k is an integer).

This means if you have 21pi/4 you can keep subtracting 2pi until the argument ends up in the principal form between -pi and pi.

Original post by davros

I presume you're working mod 2pi. What you've written isn't exactly right, is it?

Should have made it clearer in my post

Original post by Soul Wavel3ngth

could you elaborate please?

In addition to Driving_Mad's update. note that sin and cos are periodic with period 2pi, so you can add/subtract multiples of 2pi from any value you have and still get the same answer when you take the sine or cosine, so e.g. sin(21pi/4) = sin(21pi/4 - 2pi) = sin(21pi/4 - 4pi) etc

Original post by davros

In addition to Driving_Mad's update. note that sin and cos are periodic with period 2pi, so you can add/subtract multiples of 2pi from any value you have and still get the same answer when you take the sine or cosine, so e.g. sin(21pi/4) = sin(21pi/4 - 2pi) = sin(21pi/4 - 4pi) etc

It feels it would have been a lot clearer if the given solution had decomposed $250i\pi$ as $125(2i\pi)$ instead of $2(125i\pi)$.

- further maths question
- I’m so confused about part B Argand diagrams
- Spectroscopy help
- Is commercial law more similar to contract or trusts?
- Cu2+ and NH3 reactions
- Briggate studios - Leeds Beckett
- Confused About Elizabeth Line
- complex numbers
- How can I start a real estate business?
- Calculator not giving exact answers
- Complex numbers A level question
- Algebra
- Coordination bonds
- Can someone explain what the advanced info for Edexcel FM means
- MSc Mathematics degree - is it really post-graduate level?
- Complex numbers
- FP1 Complex Numbers
- KCL vs Coventry mental health nursing msc
- Complex numbers
- Any Difference between 'butene' and 'but-1-ene'?

- whihch one of these unis r best for supply chain management degree ?
- My face burns and itches from anything
- Official University College London Applicant Thread for 2024
- Updating admission statement to uni
- My ex wants me back but I’m seeing someone new
- Culture, Media and Creative Industries BA in KCL
- The Official Psychology Applicants for 2024 Entry Thread
- Official UCL Offer Holders Thread for 2024 entry
- Official Oxford 2024 Postgraduate Applicants Thread
- The Russell Group hurt/heal game (Part 5)
- Official KCL Offer Holders Thread for 2024 entry
- York Law Offers
- The Same Picture of Gregg Wallace Every Day (Except when I forget)
- Does anyone ever feel like their mother hates them
- Official: St George's, University of London A100 2024 Entry
- Please mark my gcse english language paper 2 question 5!!!
- PGCE maths with unrelated degree?
- Aon Industrial Placement 2024
- Official Cambridge Postgraduate Applicants 2024 Thread
- is it okay if i use edexcel physics + chem questions to add to my revision

- i made such a silly mistake I don’t know what’s wrong with me
- Oxford History DPhil applicants 2024-25
- Would you rather attend...?
- Dvla form mistake
- psychology - work experience in year 12
- Tatakae L's GYG Journey
- Cambridge ISMM 2024 entry
- NHS trust says transgender milk just as good for babies as normal milk
- my gcse adventure ⭐
- Where do I go next
- Chem a level
- Aon Graduate Scheme 2024
- The NYT games hurt/heal game
- The Forum Games Hurt/Heal Game
- Lancaster or York Psychology?
- EDEXCEL 2024 A level exams
- Maintenance Loan cancelled, thinking about leaving uni
- The Arsenal Thread XXVI
- Cambridge postgraduate application: Decision pending - application is under review
- a level business exam structure

- Mock set 4 paper 2 q14 a level maths (4 distinct points)
- UKMT Intermediate Math Challenge 2024 - Discussion
- Help with complex summation further maths a levels
- GCSE Mathematics Study Group 2023-2024
- Could I have some help with this suvat question?
- MAT practice
- A-level Mathematics Study Group 2023-2024
- Alevel Maths Question
- weird cosine question
- Series function not differentiable at a point

- hyperbolic function catenary problem
- can anyone answer this A level vectors question (very challenging)
- STEP foundation module help pls
- Ukmt IMC 2024
- ukmt imc
- This maths question is driving me crazy
- Maths Mechanics
- Confused on surds question
- HNC MATHS A2 Task 3 (Radio Transmitters)
- Senior Maths Challenge 2023

- Mock set 4 paper 2 q14 a level maths (4 distinct points)
- UKMT Intermediate Math Challenge 2024 - Discussion
- Help with complex summation further maths a levels
- GCSE Mathematics Study Group 2023-2024
- Could I have some help with this suvat question?
- MAT practice
- A-level Mathematics Study Group 2023-2024
- Alevel Maths Question
- weird cosine question
- Series function not differentiable at a point

- hyperbolic function catenary problem
- can anyone answer this A level vectors question (very challenging)
- STEP foundation module help pls
- Ukmt IMC 2024
- ukmt imc
- This maths question is driving me crazy
- Maths Mechanics
- Confused on surds question
- HNC MATHS A2 Task 3 (Radio Transmitters)
- Senior Maths Challenge 2023

The Student Room and The Uni Guide are both part of The Student Room Group.

© Copyright The Student Room 2024 all rights reserved

The Student Room and The Uni Guide are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: Imperial House, 2nd Floor, 40-42 Queens Road, Brighton, East Sussex, BN1 3XB