Question:
The conjugate of $(1+i)^3$ is:
The conjugate of $(1+i)^3$ is:
Show Hint
$(1+i)^2 = 2i$. So, $(1+i)^3 = 2i(1+i) = 2i - 2$.
Updated On: May 5, 2026
- $1+2i$
- $-2+2i$
- $-2-2i$
- $1-2i$
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Step 1: Concept
Expand the complex number $(1+i)^3$ and then find its conjugate (change the sign of the imaginary part).
Step 2: Meaning
$(1+i)^3 = 1^3 + 3i + 3i^2 + i^3 = 1 + 3i - 3 - i$.
Step 3: Analysis
$(1+i)^3 = -2 + 2i$.
Step 4: Conclusion
The conjugate of $-2 + 2i$ is $-2 - 2i$.
Final Answer: (C)
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