Consider the group <{1, -1, i, -i}, * > under multiplication. The inverse of…
2015
Consider the group <{1, -1, i, -i}, * > under multiplication. The inverse of -i is:
- A.
1
- B.
-1
- C.
i
- D.
-i
- E.
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Correct answer: C
To find the inverse of -i in the group <{1, -1, i, -i}, *>, we need to find an element x such that (-i) × x = 1.
Step 1: Recall that in complex numbers, i² = -1.
Step 2: Try multiplying -i with i: (-i) × i = -i².
Step 3: Since i² = -1, then -i² = -(-1) = 1.
Step 4: Therefore, (-i) × i = 1, which means i is the inverse of -i.
हिन्दी उत्तर:
इस समूह में -i का व्युत्क्रम वह तत्व है जिसका -i के साथ गुणा करने पर परिणाम 1 हो।
चरण 1: याद रखें कि काल्पनिक संख्या में i² = -1 होता है।
चरण 2: -i को i से गुणा करें: (-i) × i = -i²।
चरण 3: चूँकि i² = -1, तो -i² = -(-1) = 1।
चरण 4: इसलिए, (-i) × i = 1, जिसका अर्थ है कि i, -i का व्युत्क्रम है।