What is the answer to x^2=2i ?

The answer to x^2=2i is x=1+i,x=-1-i

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x^2=2i

x^{2} = 2 i

x = 1 + i, x = - 1 - i

Solution steps

x^{2} = 2 i

Substitute

x = a + bi

(a + bi)^{2} = 2 i

Expand

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

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

Rewrite

2 i

in standard complex form:

0 + 2 i

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

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

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

[a^{2} - b^{2} = 0 2 ab = 2] : (a = 1, a = - 1, b = 1 b = - 1)

Substitute back

x = a + bi

x = 1 + i, x = - 1 - i

3 x + 8 i = 12 - (12 y) i

3 x + 8 i = 12 - (16 y) i

\frac{3 + ai}{5 + bi} = 1 + 6 i

- 2 x + 6 i = (- 24 y) i - 14

∣ z - 4 i ∣ = 4