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Lesson Example Discussion Quiz: Class Homework

Quiz At Home

Title: Complex Numbers

Grade: 10-a Lesson: S2-L8

Explanation: Hello Students, time to practice and review. Let us take next 10-15 minutes to solve the ten problems using the Quiz Sheet. Then submit the quiz to get the score. This is a good exercise to check your understanding of the concepts.

Quiz: at Home

Problem Id	Problem	Options
1	Solve the equation: \$z^2 + 4z + 13 = 0\$ for z.	A) z = -3 + 2i and z = -3 - 2i B) z = 2 + 3i and z = 2 - 3i C) z = -2 + 3i and z = -2 - 3i D) z = 3 + 2i and z = 3 - 2i
2	Evaluate the expression: (1 + 2i)(3 - i).	A) 4 + 5i B) 5 + 8i C) 6 + 6i D) 5 + 5i
3	Simplify the expression: (2 + 3i)(1 - i)(3 + 4i).	A) 11 + 27i B) 11 + 23i C) 13 + 23i D) 17 + 25i
4	Perform the division: \$(4 + 3i) / (2 + i)\$.	A) \$ (11 + 2i) / 5 \$ B) \$ (13 - 4i) / 10 \$ C) \$ (-9 + 7i) / 5 \$ D) \$ (8 + 2i) / 5 \$
5	Evaluate the expression: \$ (1 + i)^5 \$.	A) - 4 - 4i B) - 2 - 2i C) - 2 - 4i D) 2 + 2i
6	Find the square of the complex number (2 + 3i).	A) 5 + i B) - 5 + 12i C) - 11 - 24i D) - 13 + 12i
7	Evaluate the following expression: \$ (1 + i)^6 / (1 - i)^3 \$.	A) 1 - 2i B) 2 + 2i C) 3 - 3i D) 4 + 4i
8	Perform the division: \$(-3 + 2i) / (1 - i)\$.	A) \$ ( 5 - i)/2 \$ B) \$ (- 5 + i)/2 \$ C) \$ (-5 - i)/2 \$ D) \$ (5 + 3i)/2 \$
9	Find the square root of the complex number z = 4 + 3i.	A) \$\pm (3/sqrt(2) + 3i 1/sqrt(2) )\$ B) \$ \pm (3/sqrt(2) - i 1/sqrt(2) ) \$ C) \$ \pm (3/sqrt(2) + i 1/sqrt(2) )\$ D) \$\pm (3/sqrt(2) - 3i 5/sqrt(2) )\$
10	Find all complex solutions to the equation: \$z^3 - 3z^2 + 7z - 5 = 0\$.	A) z = 1 - 2i B) z = 1 C) z = 1 + 2i D) All the above

Problem Id

Problem

Options

Solve the equation: \$z^2 + 4z + 13 = 0\$ for z.

A) z = -3 + 2i and z = -3 - 2i

B) z = 2 + 3i and z = 2 - 3i

C) z = -2 + 3i and z = -2 - 3i

D) z = 3 + 2i and z = 3 - 2i

Evaluate the expression: (1 + 2i)(3 - i).

A) 4 + 5i

B) 5 + 8i

C) 6 + 6i

D) 5 + 5i

Simplify the expression: (2 + 3i)(1 - i)(3 + 4i).

A) 11 + 27i

B) 11 + 23i

C) 13 + 23i

D) 17 + 25i

Perform the division: \$(4 + 3i) / (2 + i)\$.

A) \$ (11 + 2i) / 5 \$

B) \$ (13 - 4i) / 10 \$

C) \$ (-9 + 7i) / 5 \$

D) \$ (8 + 2i) / 5 \$

Evaluate the expression: \$ (1 + i)^5 \$.

A) - 4 - 4i

B) - 2 - 2i

C) - 2 - 4i

D) 2 + 2i

Find the square of the complex number (2 + 3i).

A) 5 + i

B) - 5 + 12i

C) - 11 - 24i

D) - 13 + 12i

Evaluate the following expression:
\$ (1 + i)^6 / (1 - i)^3 \$.

A) 1 - 2i

B) 2 + 2i

C) 3 - 3i

D) 4 + 4i

Perform the division: \$(-3 + 2i) / (1 - i)\$.

A) \$ ( 5 - i)/2 \$

B) \$ (- 5 + i)/2 \$

C) \$ (-5 - i)/2 \$

D) \$ (5 + 3i)/2 \$

Find the square root of the complex number z = 4 + 3i.

A) \$\pm (3/sqrt(2) + 3i 1/sqrt(2) )\$

B) \$ \pm (3/sqrt(2) - i 1/sqrt(2) ) \$

C) \$ \pm (3/sqrt(2) + i 1/sqrt(2) )\$

D) \$\pm (3/sqrt(2) - 3i 5/sqrt(2) )\$

Find all complex solutions to the equation:
\$z^3 - 3z^2 + 7z - 5 = 0\$.

A) z = 1 - 2i

B) z = 1

C) z = 1 + 2i

D) All the above