Problem: If i2=−1, then (1+i)20−(1−i)20 equals
Answer Choices:
A. −1024
B. −1024i
C. 0
D. 1024
E. 1024i
Solution:
Since i2=−1,(1+i)2=2i and (1−i)2=2i. Writing (1+i)20−(1−i)20=((1+i)2)10−((1−i)2)10. we have (1+i)20−(1−1)20=(2i)10−(−2i)10=0.