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Lesson Example Discussion Quiz: Class Homework

Quiz At Home

Title: Complex Numbers

Grade: 1300-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	Convert each number to polar form \$ - 8sqrt(2) - 8i sqrt(2) \$.	A) \$ 8 (cos (pi/4))+i (sin (pi/4)) \$ B) \$ -16 (cos (pi/4)) - i (sin (pi/4)) \$ C) \$ 16 (cos (pi/4))+i (sin (pi/4)) \$ D) \$ 16 (cos (pi/4)) - i (sin (pi/4)) \$
2	Convert each number to a rectangular form \$ 20 cis (7pi/4) \$.	A) \$ -10 sqrt(4) - 10 sqrt(2)i \$ B) \$ -11 sqrt(2) - 5 sqrt(2)i \$ C) \$ 11 sqrt(2) + 10 sqrt(2)i \$ D) \$ -10 sqrt(2) -10 sqrt(2)i \$
3	To find the Multiply equation is (2 + i)(3 − 2i).	A) 7 - i B) 8 - i C) 8 - 2i D) 9 - i
4	Solve the equation \$ z^2 + 3z +13 \$=0 for complex z.	A) \$ (-3 + sqrt(43)i)/2 \$ and \$ (-3 - sqrt(43)i)/2 \$ B) \$ (3 + sqrt(43 i)/2) \$ and \$ (3 + sqrt(43i)/2) \$ C) \$ (3 + sqrt(43 i)/7) \$ and \$ (3 + sqrt(43i)/7) \$ D) \$ (2 + sqrt(43 i)/7) \$ and \$ (2 + sqrt(43i)/7) \$
5	For each question, perform the indicated computations. Give answers in both polar and rectangular form. \$ (12 cis (pi/8))(24 cis ((5pi)/24)) \$.	A) Polar Form: \$ 288 cis (pi/3) \$ Rectangular Form: \$ 144+144 sqrt(3)i \$ B) Polar Form: \$ 288 cis (pi/3) \$ Rectangular Form: \$ 144 + 144 sqrt(4)i \$ C) Polar Form: \$ 288 cis (pi/3) \$ Rectangular Form: \$ 144 sqrt(3)i \$ D) Polar Form: \$ 288 cis (pi/4) \$ Rectangular Form: \$ 144 + 144 sqrt(3)i \$
6	Perform the indicated operation and write your answer in standard form (2 + 7i)(8 + 3i).	A) (-5 + 60i) B) (-5 + 62i) C) (-5 + 63i) D) (-2 + 64i)
7	Divide and simplify: \$5 + (3i) / 2 - i\$.	A) \$(7 / 5) - (11 / 6)i\$ B) \$(7 / 5) + (11 / 5)i\$ C) \$(8 / 5) + (11 / 5)i\$ D) \$(7 / 5) + (12 / 5)i\$
8	Perform the indicated operation and write your answer in standard form \$(1 + 5i) / (- 3i)\$.	A) \$- (5/3) + (1/4)i\$ B) \$- (7/3) + (1/3)i\$ C) \$- (5 / 3) + (1 / 3)i\$ D) \$(5/3) + (7/8)i\$
9	Perform the indicated operation and write your answer in standard form \$(6 + 7i) / (8 - i) \$.	A) \$(49/62) + (60/62)i\$ B) \$(41/66) + (12/662)i\$ C) \$(41/65) + (62/65)i\$ D) \$(49/62) - (60/62)i\$
10	Perform the indicated operation and write your answer in standard form 2i + (-8 - 15i).	A) (-7 - 17i) B) (8 + 13i) C) (7 + 17i) D) (-8 - 13i)

Problem Id

Problem

Options

Convert each number to polar form \$ - 8sqrt(2) - 8i sqrt(2) \$.

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

B) \$ -16 (cos (pi/4)) - i (sin (pi/4)) \$

C) \$ 16 (cos (pi/4))+i (sin (pi/4)) \$

D) \$ 16 (cos (pi/4)) - i (sin (pi/4)) \$

Convert each number to a rectangular form \$ 20 cis (7pi/4) \$.

A) \$ -10 sqrt(4) - 10 sqrt(2)i \$

B) \$ -11 sqrt(2) - 5 sqrt(2)i \$

C) \$ 11 sqrt(2) + 10 sqrt(2)i \$

D) \$ -10 sqrt(2) -10 sqrt(2)i \$

To find the Multiply equation is (2 + i)(3 − 2i).

A) 7 - i

B) 8 - i

C) 8 - 2i

D) 9 - i

Solve the equation \$ z^2 + 3z +13 \$=0 for complex z.

A) \$ (-3 + sqrt(43)i)/2 \$ and \$ (-3 - sqrt(43)i)/2 \$

B) \$ (3 + sqrt(43 i)/2) \$ and \$ (3 + sqrt(43i)/2) \$

C) \$ (3 + sqrt(43 i)/7) \$ and \$ (3 + sqrt(43i)/7) \$

D) \$ (2 + sqrt(43 i)/7) \$ and \$ (2 + sqrt(43i)/7) \$

For each question, perform the indicated computations. Give answers in both polar and rectangular form. \$ (12 cis (pi/8))(24 cis ((5pi)/24)) \$.

A) Polar Form: \$ 288 cis (pi/3) \$
Rectangular Form: \$ 144+144 sqrt(3)i \$

B) Polar Form: \$ 288 cis (pi/3) \$
Rectangular Form: \$ 144 + 144 sqrt(4)i \$

C) Polar Form: \$ 288 cis (pi/3) \$
Rectangular Form: \$ 144 sqrt(3)i \$

D) Polar Form: \$ 288 cis (pi/4) \$
Rectangular Form: \$ 144 + 144 sqrt(3)i \$

Perform the indicated operation and write your answer in standard form (2 + 7i)(8 + 3i).

A) (-5 + 60i)

B) (-5 + 62i)

C) (-5 + 63i)

D) (-2 + 64i)

Divide and simplify: \$5 + (3i) / 2 - i\$.

A) \$(7 / 5) - (11 / 6)i\$

B) \$(7 / 5) + (11 / 5)i\$

C) \$(8 / 5) + (11 / 5)i\$

D) \$(7 / 5) + (12 / 5)i\$

Perform the indicated operation and write your answer in standard form \$(1 + 5i) / (- 3i)\$.

A) \$- (5/3) + (1/4)i\$

B) \$- (7/3) + (1/3)i\$

C) \$- (5 / 3) + (1 / 3)i\$

D) \$(5/3) + (7/8)i\$

Perform the indicated operation and write your answer in standard form \$(6 + 7i) / (8 - i) \$.

A) \$(49/62) + (60/62)i\$

B) \$(41/66) + (12/662)i\$

C) \$(41/65) + (62/65)i\$

D) \$(49/62) - (60/62)i\$

Perform the indicated operation and write your answer in standard form 2i + (-8 - 15i).

A) (-7 - 17i)

B) (8 + 13i)

C) (7 + 17i)

D) (-8 - 13i)