Examples

Finding all 4th roots of 16

Compute all the roots of .

Solution

Write .

Evaluate roots formula:

Simplify:

Finding 2nd roots of 2i

Find both roots of .

Solution

Write .

Evaluate roots formula:

Compute the options: :

Convert to rectangular:

Some roots of unity

Find the and and and and and roots of the number .

Solution

(1)

Write . Evaluate roots formula. There is no possible :

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(2)

Write . Evaluate roots formula in terms of :

Compute the two options, :

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(3)

Evaluate roots formula in terms of :

Compute the options: :

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(4)

Evaluate roots formula:

Compute the options: :

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(5)

Evaluate roots formula:

Compute the options: :

Don’t simplify, it’s not feasible.

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(6)

Evaluate roots formula:

Compute the options: :

Simplify: