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Complex Numbers and Equations Quiz

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Questions and Answers

Which property characterizes a normal subgroup in group theory?

Invariance under conjugation (correct)

Commutativity

Closure under products

Closure under inverses

What is the concept in group theory that deals with subsets that form a group structure?

Lagrange's theorem

Cosets

Cyclic subgroups (correct)

Normal subgroups

What type of matrix has entries that are symmetric with respect to the main diagonal?

Orthogonal

Symmetric (correct)

Hermitian

Skew symmetric

Which property characterizes an integral domain in ring theory?

Every non-zero element has a multiplicative inverse Signup and view all the answers

In linear algebra, what term describes a set of vectors where one vector can be written as a linear combination of the others?

Dependent set Signup and view all the answers

What theorem states that every square matrix satisfies its own characteristic equation?

Cayley-Hamilton theorem Signup and view all the answers

What is the definition of De-Moivre's theorem?

Formula for raising a complex number to an integer or rational power Signup and view all the answers

Which group is an example of a nonabelian group?

Permutation group S3 Signup and view all the answers

What is the relationship between the arithmetic mean (AM), geometric mean (GM), and harmonic mean (HM)?

AM > GM > HM Signup and view all the answers

Which method is used to solve biquadratic equations according to the text?

Ferrari's method Signup and view all the answers

What does the m-th power theorem state?

$($AM $ imes$ GM $ imes$ HM$)^m \= ($AM$)^{2m}$ Signup and view all the answers

What is the definition of z^a in complex numbers?

$z^a = e^{(a heta)}$ Signup and view all the answers