What is the answer to x^2-8.4xi-3.15=0 ?

The answer to x^2-8.4xi-3.15=0 is x=(3(14-sqrt(161)))/(10)i,x=(3(14+sqrt(161)))/(10)i

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x^2-8.4xi-3.15=0

x^{2} - 8.4 x i - 3.15 = 0

x = \frac{3 ( 14 - 161 )}{10} i, x = \frac{3 ( 14 + 161 )}{10} i

Solution steps

x^{2} - 8.4 x i - 3.15 = 0

Substitute

x = a + bi

(a + bi)^{2} - 8.4 (a + bi) i - 3.15 = 0

Expand

(a + bi)^{2} - 8.4 (a + bi) i - 3.15 : (a^{2} - b^{2} + 8.4 b - 3.15) + i (- 8.4 a + 2 ab)

(a^{2} - b^{2} + 8.4 b - 3.15) + i (- 8.4 a + 2 ab) = 0

Rewrite

0

in standard complex form:

0 + 0 i

(a^{2} - b^{2} + 8.4 b - 3.15) + i (- 8.4 a + 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} + 8.4 b - 3.15 = 0 - 8.4 a + 2 ab = 0]

[a^{2} - b^{2} + 8.4 b - 3.15 = 0 - 8.4 a + 2 ab = 0] : a = 0, a = 0, b = \frac{3 ( 14 - 161 )}{10} b = \frac{3 ( 14 + 161 )}{10}

Substitute back

x = a + bi

x = \frac{3 ( 14 - 161 )}{10} i, x = \frac{3 ( 14 + 161 )}{10} i

z^{2} + (2 - 12 i) z + (- 1 - 9 i) = 0

x, s i g = \frac{2}{x - 3}

z^{2} (1 + i) = 2 i

z = z + \frac{i}{z}

s i (x + 3)^{2} = (x - 1)^{2} + 18

What is the answer to x^2-8.4xi-3.15=0 ?
The answer to x^2-8.4xi-3.15=0 is x=(3(14-sqrt(161)))/(10)i,x=(3(14+sqrt(161)))/(10)i