T8.2 Complex Numbers, Matrices, Vectors (QZ)

Front

What is a complex number?

Back

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is the imaginary unit, defined as i = √(-1).

Front

What is the product of (4-5i)(4+5i)?

Back

41

Front

What is a matrix?

Back

A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns, used to represent data or solve systems of equations.

Front

What is the sum of (5-2i) + (-7+8i)?

Back

-2+6i

Front

What does the term 'vector' refer to in mathematics?

Back

A vector is a quantity that has both magnitude and direction, often represented as an ordered pair (x, y) in a two-dimensional space.

Front

What is the vertical component of the vector <3,4>?

Back

4

Front

What is the horizontal component of the vector <3,4>?

Back

3

Front

What is the result of simplifying (10 + 15i) - (48 - 30i)?

Back

-38 + 45i

Front

Which product can NOT be made from matrices A and B if A is 2x3 and B is 3x2?

Back

BC (if B is 3x2 and C is 2x3, BC is valid, but if C is incompatible, it cannot be formed).

Front

What is the definition of a scalar in relation to vectors?

Back

A scalar is a real number that can multiply a vector, changing its magnitude but not its direction.