What is the answer to x^2-6i^2=0 ?

The answer to x^2-6i^2=0 is x=sqrt(6)i,x=-sqrt(6)i

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x^2-6i^2=0

x^{2} - 6 i^{2} = 0

x = 6 i, x = - 6 i

Solution steps

x^{2} - 6 i^{2} = 0

Substitute

x = a + bi

(a + bi)^{2} - 6 i^{2} = 0

Expand

(a + bi)^{2} - 6 i^{2} : (a^{2} - b^{2} + 6) + 2 iab

(a^{2} - b^{2} + 6) + 2 iab = 0

Rewrite

0

in standard complex form:

0 + 0 i

(a^{2} - b^{2} + 6) + 2 iab = 0 + 0 i

Complex numbers can be equal only if their real and imaginary parts are equalRewrite as system of equations:

[a^{2} - b^{2} + 6 = 0 2 ab = 0]

[a^{2} - b^{2} + 6 = 0 2 ab = 0] : (a = 0, a = 0, b = 6 b = - 6)

Substitute back

x = a + bi

x = 6 i, x = - 6 i

2 x^{2} + 9 x - i = 0

z^{2} = (1 + i 3)^{2}

\frac{1 + ai}{6 + bi} = 1 + 5 i

0 = \frac{1 + λi}{1 - λi}

z^{2} - (1 - 2 i) z + (2 - 16 i) = 0

What is the answer to x^2-6i^2=0 ?
The answer to x^2-6i^2=0 is x=sqrt(6)i,x=-sqrt(6)i