## anonymous 4 years ago 10. find the 4th roots of the complex number z1=1+sqrt3+i part1: write z1 in polar form part2: find the mudulus of the root of z1 part3: find the four angles that define the 4th roots of the number z1 part4: what are the fourth roots of z1=sqrt3+i

1. EarthCitizen

$z ^{4}=(1+\sqrt{3})+i$ is this the correct expression ?

2. anonymous

its acually z with a 1 at the bottom, and everything else is correct

3. EarthCitizen

$z _{1}=2.9<69.67^{o}$

4. anonymous

thats in polar form?

5. EarthCitizen

yep

6. anonymous

you know how to find the muduus

7. EarthCitizen

yh, the modulus is just adding and squaring the x and y components to find the square root of the two

8. EarthCitizen

the $|z _{1}|=2.9$

9. anonymous

ok part3 and 4?

10. EarthCitizen

yh, what's the power of z ? it should be 4 ryt, since they need four roots ?

11. anonymous

and part4

12. EarthCitizen

1.3<17.42, 1.3<107.42, 1.3<197.42 and 1.3<287.42

13. EarthCitizen

the correct angles are 17.42,107.42, 197.42 and 287.42

14. EarthCitizen

part 4. $z _{1}=\sqrt{3}+i$

15. EarthCitizen

$z _{1}= 2<30^{o}$ fourth roots in polar form 0.5<7.5, 0.5<97.5, 0.5<187.5 and 0.5<277.5

16. EarthCitizen

to convert to rectangular form, use de Moivre's theorem, $r=[\cos(\theta)+isin(\theta)]$