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Popular Algebra >

z^4=-7+24i

Solution

z^{4} = - 7 + 24 i

Solution

z = 5 cos (\frac{- arctan ( \frac{24}{7} ) + π}{4}) + 5 i sin (\frac{- arctan ( \frac{24}{7} ) + π}{4}), z = 5 cos (\frac{- arctan ( \frac{24}{7} ) + 3 π}{4}) + 5 i sin (\frac{- arctan ( \frac{24}{7} ) + 3 π}{4}), z = 5 cos (\frac{- arctan ( \frac{24}{7} ) + 5 π}{4}) + 5 i sin (\frac{- arctan ( \frac{24}{7} ) + 5 π}{4}), z = 5 cos (\frac{- arctan ( \frac{24}{7} ) + 7 π}{4}) + 5 i sin (\frac{- arctan ( \frac{24}{7} ) + 7 π}{4})

Solution steps

z^{4} = - 7 + 24 i

For

z^{n} = a

the solutions are

k = 0, 1, \dots, n - 1

For

n = 4, a = - 7 + 24 i

∣ a ∣ = 25

ar g (a) = - arctan (\frac{24}{7}) + π

Simplify

Simplify

Simplify

Simplify

z = 5 cos (\frac{- arctan ( \frac{24}{7} ) + π}{4}) + 5 i sin (\frac{- arctan ( \frac{24}{7} ) + π}{4}), z = 5 cos (\frac{- arctan ( \frac{24}{7} ) + 3 π}{4}) + 5 i sin (\frac{- arctan ( \frac{24}{7} ) + 3 π}{4}), z = 5 cos (\frac{- arctan ( \frac{24}{7} ) + 5 π}{4}) + 5 i sin (\frac{- arctan ( \frac{24}{7} ) + 5 π}{4}), z = 5 cos (\frac{- arctan ( \frac{24}{7} ) + 7 π}{4}) + 5 i sin (\frac{- arctan ( \frac{24}{7} ) + 7 π}{4})

Popular Examples

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