What is the answer to (x^2)/(2i)-2=0 ?

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

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(x^2)/(2i)-2=0

\frac{x ^{2}}{2 i} - 2 = 0

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

Solution steps

\frac{x ^{2}}{2 i} - 2 = 0

Substitute

x = a + bi

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

Multiply both sides by

2 i

\frac{( a + bi ) ^{2}}{2 i} \cdot 2 i - 2 \cdot 2 i = 0 \cdot 2 i

Simplify

(a^{2} - b^{2}) + i (- 4 + 2 ab) = 0

Rewrite

0

in standard complex form:

0 + 0 i

(a^{2} - b^{2}) + i (- 4 + 2 ab) = 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} = 0 - 4 + 2 ab = 0]

[a^{2} - b^{2} = 0 - 4 + 2 ab = 0] : (a = 2, a = - 2, b = 2 b = - 2)

Substitute back

x = a + bi

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

(x - y i)^{2} = - 8 - 6

x^{2} - 7 x + 9 y i = y^{2} i + 20 y i - 12

a + bi - 5 = i (10 + 4 (a + bi))

z^{2} + 2 i z + 3 = 0

(1 + q) (2 + i) + p = ((p + q - 1) (3 + i) + 2)

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