What is the answer to x^2=-4/3 i ?

The answer to x^2=-4/3 i is x=(sqrt(2))/(sqrt(3))-sqrt(2/3)i,x=-(sqrt(2))/(sqrt(3))+sqrt(2/3)i

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x^2=-4/3 i

x^{2} = - \frac{4}{3} i

x = \frac{2}{3} - \frac{2}{3} i, x = - \frac{2}{3} + \frac{2}{3} i

Solution steps

x^{2} = - \frac{4}{3} i

Substitute

x = a + bi

(a + bi)^{2} = - \frac{4}{3} i

Expand

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

(a^{2} - b^{2}) + 2 iab = - \frac{4}{3} i

Rewrite

- \frac{4}{3} i

in standard complex form:

0 - \frac{4}{3} i

(a^{2} - b^{2}) + 2 iab = 0 - \frac{4}{3} 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 = - \frac{4}{3}]

[a^{2} - b^{2} = 0 2 ab = - \frac{4}{3}] : a = \frac{2}{3}, a = - \frac{2}{3}, b = - \frac{2}{3} b = \frac{2}{3}

Substitute back

x = a + bi

x = \frac{2}{3} - \frac{2}{3} i, x = - \frac{2}{3} + \frac{2}{3} i

22 x - 3 y i = 3 y i + 2 x

(1 + i) (a + bi) - 2 (a - bi) = - 11 + 25 i

(1 + i) (a + 2 b) - (3 - 2 i) (a - b) = 8 + 3 i

- 4 x^{2} + 4 y^{2} i = 8 x y, z = x + i y

x^{2} - (- 2) = 7 i

What is the answer to x^2=-4/3 i ?
The answer to x^2=-4/3 i is x=(sqrt(2))/(sqrt(3))-sqrt(2/3)i,x=-(sqrt(2))/(sqrt(3))+sqrt(2/3)i