If 1+i39=a+ib, then b is equal to
1
256
0
93
Explanation for the correct option:
STEP 1: Multiply and divide (1+i3)9 by 29.
Given, 1+i39=a+ib
1+i39=291+i3929=2912+i329=29cosπ3+isinπ39
STEP 2: Apply De Moivre's theorem.
29cosπ3+isinπ39=29cos9π3+isin9π3=29cos3π+isin3π=29cosπ+isinπ=29-1+0=-29
STEP 3: Equating values of (1+i3)9 obtained in step 1 and step 2 to find a,b.
1+i39=a+ib=-29+0i
⇒ a=-29 and b=0
∴b=0
Hence option C is correct.
If (1+i√3)9=a+ib, then b is equal to
If (1+i)(1+2i)(1+3i)......(1+ni) = a+ib, then 2.5.10.....(1+n2) is equal to