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The nth roots of a complex number z₀=r*(cos(t)+isin(t)) are

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Final answer:

The nth roots of a complex number can be found using the formula for nth roots in polar form.

Step-by-step explanation:

The nth roots of a complex number z₀=r*(cos(t)+isin(t)) are given by the formula:

nth root of z₀ = √[r^(1/n) * (cos(t/n) + isin(t/n))]

For example, if we have a complex number z₀ = 4*(cos(π/4) + isin(π/4)), the square roots of z₀ would be:

√[4^(1/2) * (cos(π/4) + isin(π/4))] = √[2 * (cos(π/8) + isin(π/8))] = √[2 * (cos(22.5°) + isin(22.5°))]

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