Answer:
Remeber, the expansion of [tex](x+y)^n=\sum_{k=0}^n\binom{n}{k}x^{n-k}y^k[/tex]
Then:
[tex](1+i)^7=\sum_{k=0}^7\binom{7}{k}1^{7-k}i^k=\sum_{k=0}^7\binom{7}{k}i^k\\=\binom{7}{0}i^0+\binom{7}{1}i^1+\binom{7}{2}i^2+\binom{7}{3}i^3+\binom{7}{4}i^4+\binom{7}{5}i^5+\binom{7}{6}i^6+\binom{7}{7}i^7\\=1+7(i)+21(-1)+35(-i)+35(1)+21(i)+7(-1)+1(-i)\\=8-8i[/tex]
and
[tex](1-i)^7=\sum_{k=0}^7\binom{7}{k}1^{7-k}(-i)^k=\sum_{k=0}^7\binom{7}{k}(-1)^ki^k\\=\binom{7}{0}i^0-\binom{7}{1}i^1+\binom{7}{2}i^2-\binom{7}{3}i^3+\binom{7}{4}i^4-\binom{7}{5}i^5+\binom{7}{6}i^6-\binom{7}{7}i^7\\=1-7(i)+21(-1)-35(-i)+35(1)-21(i)+7(-1)-1(-i)\\=8+8i[/tex]
Then
[tex](1+i)^7-(1-i)^7=8-8i-(8+8i)=8-8i-8-8i=0-16i[/tex], where a=0 and b=-16
