Find the Quotient and Write in Rectangular Form $$\frac { 20 \left( \cos 45 ^ { \circ } + i \sin 45 ^ { \circ } \right) } { 5 \left( \cos 135 ^ { \circ } + i \sin 135 ^ { \circ } \right) }$$

question 52

Multiple Choice

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form.
- $$\frac { 20 \left( \cos 45 ^ { \circ } + i \sin 45 ^ { \circ } \right) } { 5 \left( \cos 135 ^ { \circ } + i \sin 135 ^ { \circ } \right) }$$

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

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Definitions:

Regret Avoidance

Notion from behavioral finance that individuals who make decisions that turn out badly will have more regret when that decision was more unconventional.

Overconfidence

A cognitive bias where an individual overestimates their abilities or the precision of their knowledge, often leading to mistakes in judgment.

Behavioral Biases

Psychological tendencies that affect investment decisions and financial behaviors.

Fundamental Risk

Risk that even if an asset is mispriced, there is still no arbitrage opportunity because the mispricing can widen before the price eventually converges to intrinsic value.