Find the Quotient and Write in Rectangular Form $$\frac { 2 \left( \cos 120 ^ { \circ } + i \sin 120 ^ { \circ } \right) } { 4 \left( \cos 60 ^ { \circ } + i \sin 60 ^ { \circ } \right) }$$

question 300

Multiple Choice

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form.
- $$\frac { 2 \left( \cos 120 ^ { \circ } + i \sin 120 ^ { \circ } \right) } { 4 \left( \cos 60 ^ { \circ } + i \sin 60 ^ { \circ } \right) }$$

• A) \(\frac { 1 } { 4 } - \frac { 1 } { 4 } \mathrm { i } \sqrt { 3 }\)
• B) \(\frac { 1 } { 4 } + \frac { 1 } { 4 } \mathrm { i } \sqrt { 3 }\)
• C) \(\frac { 1 } { 2 } \sqrt { 3 } - \frac { 1 } { 4 } \mathrm { i }\)
• D) \(\frac { 1 } { 2 } \sqrt { 3 } + \frac { 1 } { 4 } \mathrm { i }\)

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Definitions:

Angiosperm

A group of plants that have flowers and produce seeds enclosed within a carpel; the largest group of plants on Earth.

Carpels

The female reproductive organ of a flower, consisting of an ovary, a stigma, and usually a style.

Mature Ovary

The part of the female reproductive organ in angiosperms that has completed its development phase, typically containing the ovules and ready for fertilization.

Stigmatized Pollen Grain

a pollen grain that has been rejected or marked negatively by stigma cells, potentially due to species incompatibility in plant reproduction.