What is the answer to x^2+6+(2x)i=15+6i ?

The answer to x^2+6+(2x)i=15+6i is x=3,x=-3-2i

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x^2+6+(2x)i=15+6i

x^{2} + 6 + (2 x) i = 15 + 6 i

x = 3, x = - 3 - 2 i

Solution steps

x^{2} + 6 + (2 x) i = 15 + 6 i

Substitute

x = a + bi

(a + bi)^{2} + 6 + 2 (a + bi) i = 15 + 6 i

Expand

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

(a^{2} - b^{2} + 6 - 2 b) + i (2 a + 2 ab) = 15 + 6 i

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

[a^{2} - b^{2} + 6 - 2 b = 15 2 a + 2 ab = 6]

[a^{2} - b^{2} + 6 - 2 b = 15 2 a + 2 ab = 6] : (a = 3, a = - 3, b = 0 b = - 2)

Substitute back

x = a + bi

x = 3, x = - 3 - 2 i

i = \frac{70 \cdot 10 e ^{- 9}}{5 s}

e = \frac{( i \cdot n ^{2} )}{( 179 )}

(x + y i)^{2} = 4 i

x + - 64 = 3 + y i

(1 + i) z^{2} + z - 5 = 0

What is the answer to x^2+6+(2x)i=15+6i ?
The answer to x^2+6+(2x)i=15+6i is x=3,x=-3-2i