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Complex numbers and matrices
8 ECAT Mathematics questions with answers and explanations.
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What is i^7, where i is the square root of -1?
- 1 i
- 2 -i
- 3 1
- 4 -1
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What is the modulus of the complex number 3 + 4i?
- 1 7
- 2 25
- 3 5
- 4 1
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What is (2 + 3i)(2 - 3i)?
- 1 13
- 2 -5
- 3 4 - 9i
- 4 -13
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What is the determinant of the matrix [[2, 3], [1, 4]]?
- 1 11
- 2 5
- 3 8
- 4 -5
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What is the complex conjugate of 5 - 2i?
- 1 -5 + 2i
- 2 5 + 2i
- 3 -5 - 2i
- 4 2 - 5i
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Correct answer: 5 + 2i
The conjugate changes the sign of the imaginary part, giving 5 + 2i.
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The matrix [[1, 2], [2, 4]] is:
- 1 The identity matrix
- 2 Invertible
- 3 Singular
- 4 A zero matrix
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Correct answer: Singular
Its determinant is 1 x 4 - 2 x 2 = 0, so it has no inverse and is singular.
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What is (1 + i)^2?
- 1 2
- 2 1 + 2i
- 3 0
- 4 2i
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If I is the 2 x 2 identity matrix and A is any 2 x 2 matrix, then I A equals:
- 1 The zero matrix
- 2 A
- 3 A transposed
- 4 The inverse of A
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Correct answer: A
Multiplying by the identity leaves a matrix unchanged.