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Complex Numbers and Matrices Quiz

Authored by Mohamed Youssef

Mathematics

11th Grade

CCSS covered

Used 1+ times

Complex Numbers and Matrices Quiz
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23 questions

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1.

MULTIPLE CHOICE QUESTION

1 min • 10 pts

Identify the complex number from the following options:

Answer explanation

A complex number has a real part and an imaginary part. Among the options, '4i' is purely imaginary, while the others are real numbers. Therefore, '4i' is the only complex number.

2.

MULTIPLE CHOICE QUESTION

1 min • 10 pts

Answer explanation

To convert the complex number 5 + 12i to polar form, we find the modulus r = √(5² + 12²) = 13 and the angle θ = tan⁻¹(12/5). Thus, the correct choice is 13(\cos \theta + i\sin \theta) where θ = tan⁻¹(12/5).

3.

MULTIPLE CHOICE QUESTION

1 min • 10 pts

Answer explanation

To add the complex numbers -3 + 7i and 6 - 2i, combine the real parts: -3 + 6 = 3, and the imaginary parts: 7i - 2i = 5i. Thus, the result is 3 + 5i, which matches the correct answer.

4.

MULTIPLE CHOICE QUESTION

1 min • 10 pts

Answer explanation

To multiply (2 + 3i) and (4 + 5i), use the distributive property: (2*4) + (2*5i) + (3i*4) + (3i*5i). This simplifies to 8 + 10i + 12i - 15 = -7 + 22i. The correct answer is -7 + 23i.

5.

MULTIPLE CHOICE QUESTION

1 min • 10 pts

Answer explanation

To add the matrices, sum corresponding elements: \begin{bmatrix} 2+6 & 3+7 \ 4+8 & 5+9 \end{bmatrix} = \begin{bmatrix} 8 & 10 \ 12 & 14 \end{bmatrix}. Thus, the correct answer is \begin{bmatrix} 8 & 10 \ 12 & 14 \end{bmatrix}.

6.

MULTIPLE CHOICE QUESTION

1 min • 10 pts

Answer explanation

To multiply the matrices, calculate each element: (1*0 + 3*1) = 3, (1*2 + 3*3) = 11, (2*0 + 4*1) = 4, (2*2 + 4*3) = 14. Thus, the result is \begin{bmatrix} 3 & 11 \ 4 & 14 \end{bmatrix}, which matches the correct answer.

7.

MULTIPLE CHOICE QUESTION

1 min • 10 pts

Identify the complex number from the following options:

Answer explanation

The complex number is defined as a number in the form a + bi, where i is the imaginary unit. Among the options, -2i is purely imaginary, making it a complex number, while the others are real numbers.

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