Online Course Discussion Forum
II-B Complex Numbers 4.17, 4.26, 4.28
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.
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!
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