Practice Test (complex numbers and matrices )

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What is a complex number?

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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^2 = -1.

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What is the imaginary unit?

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The imaginary unit, denoted as i, is defined as the square root of -1. It is used to extend the real number system to include solutions to equations that do not have real solutions.

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How do you add complex numbers?

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

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What is a matrix?

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

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What are the dimensions of a matrix?

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The dimensions of a matrix are given by the number of rows and columns it contains, expressed as 'rows x columns'. For example, a 2x3 matrix has 2 rows and 3 columns.

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What is matrix addition?

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Matrix addition involves adding corresponding elements of two matrices of the same dimensions. For example, if A = [[1, 2], [3, 4]] and B = [[5, 6], [7, 8]], then A + B = [[6, 8], [10, 12]].

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What is matrix multiplication?

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Matrix multiplication involves taking the dot product of rows and columns of two matrices. The number of columns in the first matrix must equal the number of rows in the second matrix.

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What is the conjugate of a complex number?

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The conjugate of a complex number a + bi is a - bi. It is used in various operations, including division of complex numbers.

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How do you multiply complex numbers?

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

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