Find the Quotient and Write in Rectangular Form $$\frac { 20 \left( \cos 45 ^ { \circ } + i \sin 45 ^ { \circ } \right) } { 4 \left( \cos 135 ^ { \circ } + i \sin 135 ^ { \circ } \right) }$$

question 11

Multiple Choice

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form.
- $$\frac { 20 \left( \cos 45 ^ { \circ } + i \sin 45 ^ { \circ } \right) } { 4 \left( \cos 135 ^ { \circ } + i \sin 135 ^ { \circ } \right) }$$

• A) \(- 5 \mathrm { i }\)
• B) \(5 \sqrt { 2 } - 5 i \sqrt { 2 }\)
• C) \(5 \mathrm { i }\)
• D) \(- 5 \mathrm { i } \sqrt { 2 }\)

---

Definitions:

Extended Family

A family group that extends beyond the nuclear family, including grandparents, aunts, uncles, and other relatives, who often live nearby or in one household.

Son-In-Law

A son-in-law is the husband of one's daughter, forming an integral part of the family relationship through marriage.

Family Forms

Variations in the structure and composition of families, including nuclear, single-parent, extended, and blended families, among others.

Resiliency

The ability to recover quickly from difficulties or to adapt successfully to adversity or change.