MYTUTOR SUBJECT ANSWERS

260 views

solve z^4=2(1+isqrt(3)) giving roots in form r(cos(theta)+isin(theta))

Sorry but it's a little hard to write the question out! I have the working on paper but I can't upload it. 

Ok so first you need to multiply out the brackets to make it a little easeier to look at and obtain the form z^4 = 2+2sqrt(3)i.

From here you can get a modulus of 4 and an angle of 1/3pi rad using a^2+b^2=C^2 and tan^-1 of b/a respectivley.

Remember that a+bi = mode^argi where mod is the modulus (sqrt(a^2+b^2)) and arg is the argument (tan^-1(b/a)).

From here use the identity to get exponential form and calculate Z, Z^4 = 4e^(1/3pi*i) so Z=4^(1/4)exp((1/3pi+2kpi)*i/4) = sqrt(2)*(e^(1/12pi*i), e^(7/12pi*i),e^(13/12pi*i),e^(19/12pi*i) This all looks very difficult especially without the use of an argand diagram and with only text to illustrate the equations but remember it all breaks down quite easily and all we've done is convert it to polar.

Lastly use cos(theta)+isin(theta) identity with calculated thetas to give requested form. 

Robert L. A Level Maths tutor, GCSE Maths tutor, A Level Physics tuto...

8 months ago

Answered by Robert, a GCSE Maths tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist

327 SUBJECT SPECIALISTS

£22 /hr

Sarah O.

Degree: PhD in Physics (Doctorate) - Cambridge University

Subjects offered: Maths, Physics+ 1 more

Maths
Physics
Chemistry

“I'm a first year Physics PhD student at the University of Cambridge. I completed my MChem (Chemistry degree) at the University of Warwick, for which I achieved a 1st. I have experience tutoring A-Level students Chemistry and Maths one...”

MyTutor guarantee

£18 /hr

Matthew M.

Degree: Engineering Mathematics (Bachelors) - Bristol University

Subjects offered: Maths, Law+ 1 more

Maths
Law
History

“I am an Engineering Math student at the University of Bristol. I have a range of interests, which cover maths, history and law, and would love to help others in these areas as well as encourage the same enthusiasm I have in others! I a...”

MyTutor guarantee

£18 /hr

Katy M.

Degree: English Language and Literature (Bachelors) - Oxford, Exeter College University

Subjects offered: Maths, History+ 4 more

Maths
History
English Literature
Economics
.ELAT

“My name is Katy, and I study English Langauge and Literature at the University of Oxford. I absolutely love my course, and the prospect of being able to help others with either English Language or English Literature is an appealing one...”

About the author

Robert L.

Currently unavailable: for regular students

Degree: Natural Sciences (Masters) - Durham University

Subjects offered: Maths, Physics+ 1 more

Maths
Physics
Geography

“Mathematically minded Durham Natural Scientist with fantastic A-Level results I could pass on to you! Full marks in 3/4 Geography exams, FP3 and M2.Super experienced tutor, helped students independently whilst in sixth form, voluteer...”

You may also like...

Posts by Robert

differentiate x^3(1+x)^5 with respect for x

Evaluate how plate tectonics theory helps our understanding of the distribution of seismic and volcanic events.

How would you use electron diffraction to estimate nuclear diameter

solve z^4=2(1+isqrt(3)) giving roots in form r(cos(theta)+isin(theta))

Other GCSE Maths questions

How do you find the length of a side of a right angled triangle when given the other two side lengths?

Where does the quadratic equation come from?

Solve 7(k – 3) = 3k – 5

Solve the equations giving your answer in 2d.p (5 Marks).: x^2 + y^2 = 36 , x = 2y + 6

View GCSE Maths tutors

Cookies:

We use cookies to improve our service. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok