What are the solutions to the equation z^4-49=0 ?

The solutions to the equation z^4-49=0 are z=sqrt(7),z=-sqrt(7),z=sqrt(7)i,z=-sqrt(7)i

Find the zeros of z^4-49=0

The zeros of z^4-49=0 are z=sqrt(7),z=-sqrt(7),z=sqrt(7)i,z=-sqrt(7)i

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z^{4} - 49 = 0

z = 7, z = - 7, z = 7 i, z = - 7 i

Solution steps

z^{4} - 49 = 0

Move

49

to the right side

z^{4} = 49

Rewrite the equation with

u = z^{2}

and

u^{2} = z^{4}

u^{2} = 49

Solve

u^{2} = 49 : u = 49, u = - 49

u = 49, u = - 49

Substitute back

u = z^{2},

solve for

z

Solve

z^{2} = 49 : z = 7, z = - 7

Solve

z^{2} = - 49 : z = 7 i, z = - 7 i

The solutions are

z = 7, z = - 7, z = 7 i, z = - 7 i

0.000004 x^{3} - 400 = 0

2 x (64 x^{2}) - 8 x^{2} (8 x) = 1

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

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

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

What are the solutions to the equation z^4-49=0 ?
The solutions to the equation z^4-49=0 are z=sqrt(7),z=-sqrt(7),z=sqrt(7)i,z=-sqrt(7)i
Find the zeros of z^4-49=0
The zeros of z^4-49=0 are z=sqrt(7),z=-sqrt(7),z=sqrt(7)i,z=-sqrt(7)i