What is the answer to 3x^2-125ix-3500=121ix+1543 ?

The answer to 3x^2-125ix-3500=121ix+1543 is x=41i

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3x^2-125ix-3500=121ix+1543

3 x^{2} - 125 i x - 3500 = 121 i x + 1543

x = 41 i

Solution steps

3 x^{2} - 125 i x - 3500 = 121 i x + 1543

Substitute

x = a + bi

3 (a + bi)^{2} - 125 i (a + bi) - 3500 = 121 i (a + bi) + 1543

Expand

(3 a^{2} - 3 b^{2} + 125 b - 3500) + i (- 125 a + 6 ab) = (- 121 b + 1543) + 121 ia

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

[3 a^{2} - 3 b^{2} + 125 b - 3500 = - 121 b + 1543 - 125 a + 6 ab = 121 a]

[3 a^{2} - 3 b^{2} + 125 b - 3500 = - 121 b + 1543 - 125 a + 6 ab = 121 a] : (a = 0, b = 41)

Substitute back

x = a + bi

x = 41 i

a - bi = - b + ia

a - bi - 6 ai - 6 b i^{2} = 5 + 5 i

4 (3 + 6 i)^{2} + a (3 + 6 i) + b = 0

x, (2 - i) x + 8 x^{2} = 0

z = 2 e^{i \frac{2 π}{3}}

What is the answer to 3x^2-125ix-3500=121ix+1543 ?
The answer to 3x^2-125ix-3500=121ix+1543 is x=41i