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Lesson Example Discussion Quiz: Class Homework

Quiz In Class

Title: Complex Numbers

Grade: 1400-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: in Class

Problem Id	Problem	Options
1	Find the solution. \$(3 / 2 - (1 / 3)i) - (5 / 4 + (7 / 9)i)\$.	A) \$(1 / 5) - (10 / 6)i\$ B) \$(2 / 9) + (1 / 6)i\$ C) \$(1 / 4) - (10 / 9)i\$ D) \$(2 / 9) - (1 / 6)i\$
2	Find the solution. (3 + 2i) + (3 - 8i) - (-4 - 7i).	A) (5 + i) B) (10 - i) C) (5 - i) D) (10 + i)
3	Find the solution. \$(6 + 2i)^2\$.	A) (22 + 23i) B) (32 + 24i) C) (22 - 23i) D) (32 - 24i)
4	Find the solution. \$(4 + 5i) / (4 - 5i)\$.	A) \$(-9 / 41) + (40 / 41)i\$ B) \$(8/41) + (41/40)i\$ C) \$(8/41) - (41/40)i\$ D) \$(-9 / 41) - (40 / 41)i\$
5	Find the solution. \$(i(10 - 12i)) / ((2 + i)(-1 + 4i))\$.	A) \$(-2 / 85) - (144 / 85)i\$ B) \$(10/17) - (24/85)i\$ C) \$(12/19) - (42/85)i\$ D) \$(12/19) + (42/85)i\$
6	Find the product \$ (4+3i)/(2-i) \$	A) 1 + i B) 1 + 2i C) 6 + 3i D) 6 - 3i
7	Convert each number to polar form. \$ 4sqrt(2) - 4i sqrt(2) \$	A) \$ 6( cos(pi/2) + i sin (pi/5)) \$ B) \$ 8( cos(-pi/4)+i sin (-pi/4)) \$ C) \$ 6( cos(pi/2) - i sin (pi/5)) \$ D) \$ 2( cos(pi/2) - i sin (pi/5)) \$
8	Convert each number to rectangular form \$ (6 cis ((2pi)/3))^3 \$	A) 214 B) 215 C) 216 D) 217
9	Find the quotient \$ z_1/z_2 \$ if \$ z_1 = 12 cis ((2pi)/3) \$ and \$ z_2 = 10 cis((3pi)/4) \$.	A) \$ (3/5) cis(-pi/12) \$ B) \$ (6/5) cis(-pi/8) \$ C) \$ (6/5) cis(-pi/12) \$ D) \$ (1/5) cis(-pi/12) \$
10	Given that z = 1 + i, find \$z^(2024)\$	A) \$ 3^(1012)\$ B) \$ 2^(1210)\$ C) \$ 3^(1210)\$ D) \$ 2^(1012)\$

Problem Id

Problem

Options

Find the solution. \$(3 / 2 - (1 / 3)i) - (5 / 4 + (7 / 9)i)\$.

A) \$(1 / 5) - (10 / 6)i\$

B) \$(2 / 9) + (1 / 6)i\$

C) \$(1 / 4) - (10 / 9)i\$

D) \$(2 / 9) - (1 / 6)i\$

Find the solution. (3 + 2i) + (3 - 8i) - (-4 - 7i).

A) (5 + i)

B) (10 - i)

C) (5 - i)

D) (10 + i)

Find the solution. \$(6 + 2i)^2\$.

A) (22 + 23i)

B) (32 + 24i)

C) (22 - 23i)

D) (32 - 24i)

Find the solution. \$(4 + 5i) / (4 - 5i)\$.

A) \$(-9 / 41) + (40 / 41)i\$

B) \$(8/41) + (41/40)i\$

C) \$(8/41) - (41/40)i\$

D) \$(-9 / 41) - (40 / 41)i\$

Find the solution. \$(i(10 - 12i)) / ((2 + i)(-1 + 4i))\$.

A) \$(-2 / 85) - (144 / 85)i\$

B) \$(10/17) - (24/85)i\$

C) \$(12/19) - (42/85)i\$

D) \$(12/19) + (42/85)i\$

Find the product \$ (4+3i)/(2-i) \$

A) 1 + i

B) 1 + 2i

C) 6 + 3i

D) 6 - 3i

Convert each number to polar form. \$ 4sqrt(2) - 4i sqrt(2) \$

A) \$ 6( cos(pi/2) + i sin (pi/5)) \$

B) \$ 8( cos(-pi/4)+i sin (-pi/4)) \$

C) \$ 6( cos(pi/2) - i sin (pi/5)) \$

D) \$ 2( cos(pi/2) - i sin (pi/5)) \$

Convert each number to rectangular form \$ (6 cis ((2pi)/3))^3 \$

A) 214

B) 215

C) 216

D) 217

Find the quotient \$ z_1/z_2 \$ if \$ z_1 = 12 cis ((2pi)/3) \$ and \$ z_2 = 10 cis((3pi)/4) \$.

A) \$ (3/5) cis(-pi/12) \$

B) \$ (6/5) cis(-pi/8) \$

C) \$ (6/5) cis(-pi/12) \$

D) \$ (1/5) cis(-pi/12) \$

Given that z = 1 + i, find \$z^(2024)\$

A) \$ 3^(1012)\$

B) \$ 2^(1210)\$

C) \$ 3^(1210)\$

D) \$ 2^(1012)\$