What is the answer to 4i=x^2-3x+7 ?

The answer to 4i=x^2-3x+7 is x=0.64563…-2.34092…i,x=2.35436…+2.34092…i

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4i=x^2-3x+7

4 i = x^{2} - 3 x + 7

x = 0.64563 \dots - 2.34092 \dots i, x = 2.35436 \dots + 2.34092 \dots i

Solution steps

4 i = x^{2} - 3 x + 7

Substitute

x = a + bi

4 i = (a + bi)^{2} - 3 (a + bi) + 7

Expand

(a + bi)^{2} - 3 (a + bi) + 7 : (a^{2} - b^{2} - 3 a + 7) + i (- 3 b + 2 ab)

4 i = (a^{2} - b^{2} - 3 a + 7) + i (- 3 b + 2 ab)

Rewrite

4 i

in standard complex form:

0 + 4 i

0 + 4 i = (a^{2} - b^{2} - 3 a + 7) + i (- 3 b + 2 ab)

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

[0 = a^{2} - b^{2} - 3 a + 7 4 = - 3 b + 2 ab]

[0 = a^{2} - b^{2} - 3 a + 7 4 = - 3 b + 2 ab] : (a = 0.64563 \dots, a = 2.35436 \dots, b = - 2.34092 \dots b = 2.34092 \dots)

Substitute back

x = a + bi

x = 0.64563 \dots - 2.34092 \dots i, x = 2.35436 \dots + 2.34092 \dots i

(1 + i 3)^{11} = a + ib

a + bi + 0 + 0 i = a + bi

x, f i = \frac{g r}{x}

z^{2} - (5 - 4 i) z + 20 i = 0

x + i y - 2 i - 3 = x + i y + 2 i + 3

What is the answer to 4i=x^2-3x+7 ?
The answer to 4i=x^2-3x+7 is x=0.64563…-2.34092…i,x=2.35436…+2.34092…i