What are the solutions to the equation x^2=sqrt(-16) ?

The solutions to the equation x^2=sqrt(-16) are x=sqrt(2)+sqrt(2)i,x=-sqrt(2)-sqrt(2)i

Find the zeros of x^2=sqrt(-16)

The zeros of x^2=sqrt(-16) are x=sqrt(2)+sqrt(2)i,x=-sqrt(2)-sqrt(2)i

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x^{2} = - 16

x = 2 + 2 i, x = - 2 - 2 i

Solution steps

x^{2} = - 16

Simplify

- 16 : 4 i

For

z^{n} = a

the solutions are

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

For

n = 2, a = 4 i

∣ a ∣ = 4

ar g (a) = \frac{π}{2}

x = 4 (cos (\frac{\frac{π}{2} + 2 \cdot 0 π}{2}) + i sin (\frac{\frac{π}{2} + 2 \cdot 0 π}{2})), x = 4 (cos (\frac{\frac{π}{2} + 2 \cdot 1 π}{2}) + i sin (\frac{\frac{π}{2} + 2 \cdot 1 π}{2}))

Simplify

4 (cos (\frac{\frac{π}{2} + 2 \cdot 0 π}{2}) + i sin (\frac{\frac{π}{2} + 2 \cdot 0 π}{2})) : 2 + 2 i

Simplify

4 (cos (\frac{\frac{π}{2} + 2 \cdot 1 π}{2}) + i sin (\frac{\frac{π}{2} + 2 \cdot 1 π}{2})) : - 2 - 2 i

x = 2 + 2 i, x = - 2 - 2 i

x^{2} + 8 x + 25 = 0

8 x^{2} + 9 = 313

16 x^{2} - 25 = 0

3 x^{2} + 18 = 15 x

x^{2} - 2 x - 3 = - 4

What are the solutions to the equation x^2=sqrt(-16) ?
The solutions to the equation x^2=sqrt(-16) are x=sqrt(2)+sqrt(2)i,x=-sqrt(2)-sqrt(2)i
Find the zeros of x^2=sqrt(-16)
The zeros of x^2=sqrt(-16) are x=sqrt(2)+sqrt(2)i,x=-sqrt(2)-sqrt(2)i