Problem: If i2=−1, then the sum cos45∘+icos135∘+…+incos(45+90n)∘+ …+i40cos3645∘ equals
Answer Choices:
A. 22
B. −10i2
C. 2212
D. 22(21−20i)
E. 22(21+20i)
Solution:
Since
incos(45+90n)∘=⎩⎪⎪⎨⎪⎪⎧22,n even 2−i2,n odd
the sum is 22(21−20i).