SOLUTION: if i represents the imaginary number whose square is -1,then (radical2 + radical2 x i)^4= ?

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: if i represents the imaginary number whose square is -1,then (radical2 + radical2 x i)^4= ?       Log On


   

Question 148523: if i represents the imaginary number whose square is -1,then (radical2 + radical2 x i)^4= ?
Found 2 solutions by vleith, Earlsdon:
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
%28sqrt%282%29%2Asqrt%282%29%2Ai%29%5E4 =
%282%2Ai%29%5E4 =
%282%5E4+%2Ai%5E4%29 =
16+%2Ai%5E%282%2B2%29 =
16+%2Ai%5E2+%2A+i%5E2 =
16+%2A%28-1%29+%2A+%28-1%29 =
16+%2A1 =
16

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Evaluate:
%28sqrt%282%29%2Bsqrt%282%29i%29%5E4
It's easier if you first find the square using foil:
=2%2B2i%2B2i%2B2i%5E2 but i%5E2+=+1, so...
4%2B4i Now square this.
%284%2B4i%29%5E2+=+16%2B16i%2B16i%2B16i%5E2 which simplifies to:
32%2B32i