Question:
The value of \((1 + i)^{10}\) is equal to
The value of \((1 + i)^{10}\) is equal to
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Use polar form or square repeatedly: \((1+i)^2 = 2i\) simplifies powers.
Updated On: Apr 25, 2026
- 16
- 16i
- 32
- 32i
- 64
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the Concept:
\((1+i)^2 = 1 + 2i + i^2 = 2i\). So \((1+i)^{10} = [(1+i)^2]^5 = (2i)^5\).
Step 2: Detailed Explanation:
\((2i)^5 = 32 \cdot i^5 = 32 \cdot i\) because \(i^5 = i\). Thus \(32i\).
Step 3: Final Answer:
Option (D).
\((1+i)^2 = 1 + 2i + i^2 = 2i\). So \((1+i)^{10} = [(1+i)^2]^5 = (2i)^5\).
Step 2: Detailed Explanation:
\((2i)^5 = 32 \cdot i^5 = 32 \cdot i\) because \(i^5 = i\). Thus \(32i\).
Step 3: Final Answer:
Option (D).
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