Find All the Complex Roots $- 16$ A) B) C) D)

question 222

Multiple Choice

Find all the complex roots. Leave your answers in polar form with the argument in degrees.
-The complex fourth roots of $- 16$

• A) \(2 \left( \cos 45 ^ { \circ } + i \sin 45 ^ { \circ } \right) , 2 \left( \cos 135 ^ { \circ } + i \sin 135 ^ { \circ } \right) , 2 \left( \cos 225 ^ { \circ } + i \sin 225 ^ { \circ } \right) , 16 \left( \cos 315 ^ { \circ } + i \sin 315 ^ { \circ } \right)\)
• B) \(\sqrt [ 4 ] { 2 } \left( \cos 45 ^ { \circ } + i \sin 45 ^ { \circ } \right) , \sqrt [ 4 ] { 2 } \left( \cos 135 ^ { \circ } + i \sin 135 ^ { \circ } \right) , \sqrt [ 4 ] { 2 } \left( \cos 225 ^ { \circ } + i \sin 225 ^ { \circ } \right) , \sqrt [ 4 ] { 2 } \left( \cos 315 ^ { \circ } + i \sin 315 ^ { \circ } \right)\)
• C) \(2 \left( \cos 90 ^ { \circ } + i \sin 90 ^ { \circ } \right) , 2 \left( \cos 180 ^ { \circ } + i \sin 180 ^ { \circ } \right) , 2 \left( \cos 270 ^ { \circ } + i \sin 270 ^ { \circ } \right) , 2 \left( \cos 360 ^ { \circ } + i \sin 360 ^ { \circ } \right)\)
• D) \(16 \left( \cos 45 ^ { \circ } + i \sin 45 ^ { \circ } \right) , 16 \left( \cos 135 ^ { \circ } + i \sin 135 ^ { \circ } \right) , 16 \left( \cos 225 ^ { \circ } + i \sin 225 ^ { \circ } \right) , 16 \left( \cos 315 ^ { \circ } + i \sin 315 ^ { \circ } \right)\)

---

Definitions:

Sensorimotor Stages

The first stage of Piaget's theory of cognitive development, spanning from birth to approximately age 2, where infants learn about the world through their senses and motor actions.

Infant's Interaction

The ways in which a baby engages with their environment and people around them, crucial for social and cognitive development.

Sensorimotor Stages

The first of Jean Piaget's four stages of cognitive development, during which infants learn through interacting with the environment.

Adapt

To adjust or change in response to new or different conditions.