Divide the Complex Numbers Below and Leave the Result in Trigonometric

question 51

Multiple Choice

Divide the complex numbers below and leave the result in trigonometric form. $$\frac { 4 ( \cos ( 7 \pi / 10 ) + i \sin ( 7 \pi / 10 ) ) } { 10 ( \cos ( 3 \pi / 7 ) + i \sin ( 3 \pi / 7 ) ) }$$

• A) \(\cos \frac { 79 } { 70 } \pi + i \sin \frac { 79 } { 70 } \pi\) ​
• B)​ \(\cos \frac { 19 } { 70 } \pi + i \sin \frac { 19 } { 70 } \pi\)
• C)​ \(\frac { 2 } { 5 } \left( \cos \frac { 79 } { 70 } \pi + i \sin \frac { 79 } { 70 } \pi \right)\)
• D)​ \(\frac { 2 } { 5 } \left( \cos \frac { 2 } { 35 } \pi + i \sin \frac { 2 } { 35 } \pi \right)\)
• E)​ \(\frac { 2 } { 5 } \left( \cos \frac { 19 } { 70 } \pi + i \sin \frac { 19 } { 70 } \pi \right)\)

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Definitions:

Malaria

Disease caused by the protozoan Plasmodium vivax; transmitted by the Anopheles mosquito.

Fungi

A kingdom of organisms that includes molds, yeasts, and mushrooms, which live by decomposing and absorbing the organic material in which they grow.

Lichens

Symbiotic associations between a fungus and a photosynthetic partner (usually an algae or cyanobacteria), living together on surfaces like rocks or trees.

Algae

A diverse group of photosynthetic organisms that are not necessarily closely related, ranging from unicellular microalgae to large multicellular forms, inhabiting both freshwater and marine environments.