Online Course Discussion Forum

II-B Complex Numbers 4.17, 4.26, 4.28

 
 
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II-B Complex Numbers 4.17, 4.26, 4.28
by Jimmy Fan - Wednesday, 22 May 2024, 12:33 PM
 

For 4.17, I don’t really get how to turn √i into polar form.

For 4.26, I got \( x^4 i+4=0 \) but I don’t think that really helps.

For 4.28, I have zero idea whatsoever what to do.

Can somebody help? Thanks.

 
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Re: II-B Complex Numbers 4.17, 4.26, 4.28
by John Lensmire - Wednesday, 22 May 2024, 1:28 PM
 

Some hints:

  • 4.17: What is $i$ in polar form? Then remember that taking the square root is the same as raising to the $1/2$ power (and De Moivre's formula still works for fractional powers.)
  • 4.26: How did you solve 4.25? Both can actually be done using a similar method. Like 4.17 start by converting 4i into polar form. Note to get all the roots, remember adding $2\pi$ or $360^\circ$ to the argument gives the same complex number.
  • 4.28: $z$ has modulus $1$, so it can be written in polar form as $\cos(\theta) + i\cdot \sin(\theta)$ for some $\theta$. Try dividing the numerator and denominator of the expression by $z^n$ so the denominator is $z^{-n} + z^{n}$ and calculate from there.

Hope these hints help!

Picture of Jimmy Fan
Re: II-B Complex Numbers 4.17, 4.26, 4.28
by Jimmy Fan - Wednesday, 22 May 2024, 11:27 PM
 

I got 4.17, IDK what I was doing earlier. 

I still don't really get 4.26 and 4.28. Can you please help me?