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^(1/3pii) so Z=4^(1/4)exp((1/3pi+2kpi)i/4) = sqrt(2)(e^(1/12pii), e^(7/12pii),e^(13/12pii),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. 

RL
Answered by Robert L. Maths tutor

6124 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

There is a quarter circle with radius 8cm, what is the area of the quarter circle. The answer should be given in terms of pi, units are cm^2.


Find where the equation y = x^2 + x - 2 crosses the x-axis.


How to solve the inequality 4(x+3) < 60?


Solve: 3x + 4 = x + 12


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning