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

The answer to i=2x^2+x-2 is x=0.80753…+0.23639…i,x=-1.30753…-0.23639…i

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i=2x^2+x-2

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

x = 0.80753 \dots + 0.23639 \dots i, x = - 1.30753 \dots - 0.23639 \dots i

Solution steps

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

Substitute

x = a + bi

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

Expand

2 (a + bi)^{2} + a + bi - 2 : (2 a^{2} - 2 b^{2} + a - 2) + i (b + 4 ab)

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

Rewrite

i

in standard complex form:

0 + i

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

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

[0 = 2 a^{2} - 2 b^{2} + a - 2 1 = b + 4 ab]

[0 = 2 a^{2} - 2 b^{2} + a - 2 1 = b + 4 ab] : (a = 0.80753 \dots, a = - 1.30753 \dots, b = 0.23639 \dots b = - 0.23639 \dots)

Substitute back

x = a + bi

x = 0.80753 \dots + 0.23639 \dots i, x = - 1.30753 \dots - 0.23639 \dots i

(a - bi) (a + bi) + (a - bi) = 3 - i

(x - y) + 8 i = 6 + y i

2 p - q + i (7 i + 3) = 2 (2 i - q) - i (p + 3 q)

y - 5 = - i [x - (- 5)]

(2 + 3 i) (x - y) i = 2 - 10 i

What is the answer to i=2x^2+x-2 ?
The answer to i=2x^2+x-2 is x=0.80753…+0.23639…i,x=-1.30753…-0.23639…i