Matrix, complex numbers and matrix

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 the square root of -1.

Front

How do you add complex numbers?

Back

To add complex numbers, combine the real parts and the imaginary parts separately. For example, (a + bi) + (c + di) = (a + c) + (b + d)i.

Front

What is the result of (7 - 2i) - (-4 + 3i)?

Back

11 - 5i.

Front

How do you subtract complex numbers?

Back

To subtract complex numbers, subtract the real parts and the imaginary parts separately. For example, (a + bi) - (c + di) = (a - c) + (b - d)i.

Front

What is matrix multiplication?

Back

Matrix multiplication involves multiplying rows of the first matrix by columns of the second matrix. The number of columns in the first matrix must equal the number of rows in the second matrix.

Front

What is the result of (-2 + 7i) + (5 - 3i)?

Back

3 + 4i.

Front

What is a vector?

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

How do you find the resultant vector from two vectors?

Back

To find the resultant vector, add the corresponding components of the vectors. For example, if vector A = and vector B = , then the resultant vector R = .

Front

What is the definition of a matrix?

Back

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

Front

What does it mean for matrices to be compatible for multiplication?

Back

Two matrices are compatible for multiplication if the number of columns in the first matrix equals the number of rows in the second matrix.