- #1
LocationX
- 147
- 0
I am asked to use the exponential form [tex]e^{i \theta}[/tex] to express the three cube roots of:
(a) 1
(b) i
(c) -i
what exactly does this question mean? I am really lost as to what they are asking for.
here is a stab at it:
(a)
cube root of 1 is 1... so... would that mean... [tex]1=e^{- \infty +i \theta[/tex]
(b)
cube root of i is [tex]\frac{\sqrt{3}}{2}+0.5i[/tex] so... [tex]\frac{\sqrt{3}}{2}+0.5i=e^{i \frac{\pi}{6}}[/tex]
(c)
cube root of -i is [tex]\frac{\sqrt{3}}{2}-0.5i[/tex] so... [tex]\frac{\sqrt{3}}{2}-0.5i=e^{-i \frac{\pi}{6}}[/tex]
is this the right way to approch this problem?
(a) 1
(b) i
(c) -i
what exactly does this question mean? I am really lost as to what they are asking for.
here is a stab at it:
(a)
cube root of 1 is 1... so... would that mean... [tex]1=e^{- \infty +i \theta[/tex]
(b)
cube root of i is [tex]\frac{\sqrt{3}}{2}+0.5i[/tex] so... [tex]\frac{\sqrt{3}}{2}+0.5i=e^{i \frac{\pi}{6}}[/tex]
(c)
cube root of -i is [tex]\frac{\sqrt{3}}{2}-0.5i[/tex] so... [tex]\frac{\sqrt{3}}{2}-0.5i=e^{-i \frac{\pi}{6}}[/tex]
is this the right way to approch this problem?