{"@context":"https://schema.org/","@type":"Quiz","dateCreated":"2025-01-06T08:37:33.768Z","dateModified":"2026-02-11T12:37:14.881Z","typicalAgeRange":"11-18","educationalLevel":"CUET (PG)","assesses":"Geophysics - Mathematics","educationalAlignment":[{"@type":"AlignmentObject","alignmentType":"educationalTopic","targetName":"Mathematics"},{"@type":"AlignmentObject","alignmentType":"educationalSubject","targetName":"Geophysics"},{"@type":"AlignmentObject","alignmentType":"educationalExam","targetName":"CUET (PG)"}],"name":"Quiz about Mathematics","about":{"@type":"Thing","name":"Geophysics - Mathematics"},"hasPart":[{"@type":"Question","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","educationalLevel":"intermediate","name":"Question About Mathematics","text":"The principal value of $$ i^i $$ is:}","encodingFormat":"text/markdown","comment":{"@type":"Comment","text":"The principal value of powers of complex numbers involves using logarithms and Euler’s formula to simplify expressions."},"suggestedAnswer":[{"@type":"Answer","position":0,"encodingFormat":"text/markdown","text":"

\$ e^{-\\pi i} \$

","comment":{"@type":"Comment","text":"\"\""}},{"@type":"Answer","position":1,"encodingFormat":"text/markdown","text":"

\$ e^{\\pi i} \$

","comment":{"@type":"Comment","text":"\"\""}},{"@type":"Answer","position":2,"encodingFormat":"text/markdown","text":"

\$ e^{-\\pi/2} \$

","comment":{"@type":"Comment","text":"\"\""}},{"@type":"Answer","position":3,"encodingFormat":"text/markdown","text":"

\$ e^{-\\pi/4} \$

","comment":{"@type":"Comment","text":"\"\""}}],"acceptedAnswer":{"@type":"Answer","position":2,"encodingFormat":"text/markdown","text":"

\$ e^{-\\pi/2} \$

","comment":{"@type":"Comment","text":"The principal value of powers of complex numbers involves using logarithms and Euler’s formula to simplify expressions."},"answerExplanation":{"@type":"comment","text":"The principal value of \$ i^i \$ is computed using the logarithmic representation of complex numbers. Euler’s formula reveals this value to be: \\[i^i = e^{-\\pi/2}.\\]"}}}]}

Firm 2	Cooperate	Compete
Firm 1	5, 5	0, 10
Compete	10,0	2, 2

The principal value of \( i^i \) is:

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The Correct Option is C

Solution and Explanation

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