Complex Quadratic Equations Flashcards (11 cards)

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1Question

What equations correspond to the square root of a complex number a=α+iβa=\alpha+i\beta?

Answer

They are x2−y2=αx^2 - y^2 = \alpha, x2+y2=α2+β2x^2 + y^2 = \sqrt{\alpha^2 + \beta^2}, and 2xy=β2xy = \beta.

2Question

What is the first step to solve z2=az^2 = a for complex zz?

Answer

Write zz as x+iyx + iy and equate real and imaginary parts.

3Question

What are the two solutions of the equation z2=3+4iz^2=3+4i?

Answer

The solutions are z=2+iz=2+i and z=−2−iz=-2-i.

4Question

What are the values of x2x^2 and y2y^2 for z2=−6−8iz^2=-6-8i?

Answer

They are x2=2x^2=2 and y2=8y^2=8 respectively.

5Question

Square root of complex number: a=α+iβ

Answer

Solve for z=x+iy: equations for x, y from complex parts.

6Question

Solutions to z²=3+4i

Answer

z=2+i and z=-2-i.

7Question

Complex quadratic formula element

Answer

Discriminant is b²-4ac, complex number.

8Question

Roots relation: sum

Answer

Sum is -b/a.

9Question

Roots relation: product

Answer

Product is c/a.

10Question

Special root condition: a+b+c=0

Answer

Roots are 1 and c/a.

11Question

Root calculation memory hook

Answer

Normalize, complete square, find Δ, then roots.

Test yourself with the quiz

Answer 8 questions on Complex Quadratic Equations.

1. For a=α+iβa=\alpha+i\beta and z=x+iyz=x+iy, which system is equivalent to z2=az^2=a?

2. When solving z2=α+iβz^2=\alpha+i\beta by writing z=x+iyz=x+iy, which procedure correctly determines the possible square roots?

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Read the study guide

Go over the full study guide for Complex Quadratic Equations.

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