Questions on Algebra: Complex Numbers answered by real tutors!

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Question 148523: if i represents the imaginary number whose square is -1,then (radical2 + radical2 x i)^4= ? : if i represents the imaginary number whose square is -1,then (radical2 + radical2 x i)^4= ?
Answer by vleith(1172) About Me  (Show Source):
You can put this solution on YOUR website!
(sqrt(2)*sqrt(2)*i)^4 =
(2*i)^4 =
(2^4 *i^4) =
16 *i^(2+2) =
16 *i^2 * i^2 =
16 *(-1) * (-1) =
16 *1 =
16
Question 148523: if i represents the imaginary number whose square is -1,then (radical2 + radical2 x i)^4= ? : if i represents the imaginary number whose square is -1,then (radical2 + radical2 x i)^4= ?
Answer by Earlsdon(3748) About Me  (Show Source):
You can put this solution on YOUR website!
Evaluate:
(sqrt(2)+sqrt(2)i)^4
It's easier if you first find the square using foil:
(sqrt(2)+sqrt(2)i)^2 = (sqrt(2)+sqrt(2)i)(sqrt(2)+sqrt(2)i)=2+2i+2i+2i^2 but i^2 = 1, so...
4+4i Now square this.
(4+4i)^2 = 16+16i+16i+16i^2 which simplifies to:
32+32i