Quadratic equations with complex roots

1003107506

Level:

Find the complex roots of the following quadratic equation.

9 x^{2} + 4 i = 0

x_{1} = - \frac{\sqrt{2}}{3} + \frac{\sqrt{2}}{3} i, x_{2} = \frac{\sqrt{2}}{3} - \frac{\sqrt{2}}{3} i

x_{1} = \frac{2}{3} i, x_{2} = - \frac{2}{3} i

x_{1} = \frac{\sqrt{2}}{3} + \frac{\sqrt{2}}{3} i, x_{2} = - \frac{\sqrt{2}}{3} - \frac{\sqrt{2}}{3} i

x_{1} = \frac{2}{3}, x_{2} = - \frac{2}{3}

1003107507

Level:

Find the solution set of the following quadratic equation in the complex plane.

x^{2} + 3 i x + 10 = 0

{- 5 i; 2 i}

{- 2 i; 5 i}

{2 - 5 i; 5 - 2 i}

{- 2 + 5 i; - 5 + 2 i}

\emptyset

1003107508

Level:

Find the complex roots of the following quadratic equation.

x^{2} + (2 + 2 i) x + 2 i = 0

x_{1, 2} = - 1 - i

x_{1, 2} = 1 + i

x_{1} = 1 + i, x_{2} = - 1 - i

x_{1} = 1 - i, x_{2} = - 1 + i

1003107509

Level:

Find the solution set of the following quadratic equation in the complex plane.

(3 - 2 i) x^{2} - (2 - 4 i) x + 2 = 0

{1 - i; \frac{1}{13} + \frac{5}{13} i}

{- 1 + i; - \frac{1}{13} - \frac{5}{13} i}

\emptyset

{- 1 + i; \frac{1}{13} + \frac{5}{13} i}

{1 - i; - \frac{1}{13} - \frac{5}{13} i}

1003107510

Level:

Find the solution set of the following quadratic equation in the complex plane.

x + \frac{i}{2} = \frac{1}{x} + \frac{2}{i}

{- \frac{1}{2} i; - 2 i}

{\frac{1}{2} i; 2 i}

{\frac{1}{2} i; - 2 i}

{- \frac{1}{2} i; 2 i}

\emptyset

1003107511

Level:

Find the solution set of the following quadratic equation in the complex plane.

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

{- \frac{1}{2} + \frac{1}{2} i; 1 + i}

{- \frac{1}{2} + i; 1 + \frac{1}{2} i}

{\frac{1}{2} - \frac{1}{2} i; - 1 - i}

{\frac{1}{2} - i; - 1 - \frac{1}{2} i}

{- \frac{1}{2} - \frac{1}{2} i; 1 - i}

{\frac{1}{2} + i; - 1 + \frac{1}{2} i}

1003109401

Level:

Which of the given quadratic equations has the roots

x_{1} = 2 + i

and

x_{2} = 1 - 3 i

x^{2} - (3 - 2 i) x + 5 - 5 i = 0

x^{2} + (3 - 2 i) x + 5 - 5 i = 0

x^{2} - (3 + 2 i) x + 5 - 5 i = 0

x^{2} + (3 + 2 i) x + 5 - 5 i = 0

1003109402

Level:

Which of the given quadratic equations has the roots

x_{1} = 1 + i

and

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

x^{2} - (1 + 3 i) x - 2 + 2 i = 0

x^{2} - (1 + 3 i) x - 2 - 2 i = 0

x^{2} - (1 + 3 i) x + 2 + 2 i = 0

x^{2} - (1 + 3 i) x + 2 - 2 i = 0

1003109403

Level:

One of the following equations has the solutions

x_{1} = \frac{1}{2} - i

and

x_{2} = - \frac{1}{2} + 2 i

. Find this equation.

4 x^{2} - 4 i x + 7 + 6 i = 0

4 x^{2} - 4 i x - 9 + 3 i = 0

4 x^{2} + 4 i x + 7 + 6 i = 0

4 x^{2} + 4 i x - 9 + 3 i = 0

1003109404

Level:

One of the roots of the quadratic equation

x^{2} + p x + 1 - 3 i = 0

with a complex parameter

p

x_{1} = - i

. Choose the equivalent form of the given equation.

(x + i) (x - 3 - i) = 0

(x + i) (x - 3 + i) = 0

(x - i) (x - 3 - i) = 0

(x + i) (x + 3 + i) = 0

(x - i) (x - 3 + i) = 0

(x - i) (x + 3 + i) = 0

Quadratic equations with complex roots

1003107506

1003107507

1003107508

1003107509

1003107510

1003107511

1003109401

1003109402

1003109403

1003109404

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