Practice Test (complex numbers and matrices )

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.

Tags

CCSS.HSN.CN.A.1

Front

What is the conjugate of a complex number?

Back

The conjugate of a complex number a + bi is a - bi. It is obtained by changing the sign of the imaginary part.

Tags

CCSS.HSN.CN.A.3

Front

How do you multiply two complex numbers?

Back

To multiply two complex numbers (a + bi) and (c + di), use the distributive property: (a + bi)(c + di) = ac + adi + bci + bdi^2. Remember that i^2 = -1.

Tags

CCSS.HSN.CN.A.2

Front

What is a matrix?

Back

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

Front

What are the dimensions of a matrix?

Back

The dimensions of a matrix are given in the form 'rows x columns'. For example, a 2x3 matrix has 2 rows and 3 columns.

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.

Tags

CCSS.HSN.VM.C.8

Front

What is the identity matrix?

Back

The identity matrix is a square matrix with ones on the diagonal and zeros elsewhere. It acts as the multiplicative identity in matrix multiplication.

Tags

CCSS.HSN.VM.C.10

Front

What is the determinant of a 2x2 matrix?

Back

For a 2x2 matrix [[a, b], [c, d]], the determinant is calculated as ad - bc.

Front

What is the sum of two matrices?

Back

The sum of two matrices is obtained by adding their corresponding elements. The matrices must have the same dimensions.

Tags

CCSS.HSN.VM.C.8

Front

What is a linear equation?

Back

A linear equation is an equation that represents a straight line when graphed. It can be written in the form ax + by = c, where a, b, and c are constants.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2