SOLUTION: Write the expression in the standard form a + bi (√2/2+√2/2i)^2 Please help me solve this equation The answer I have is a. i/2 b. -i c. i or d. -i/2 Can you he

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Write the expression in the standard form a + bi (√2/2+√2/2i)^2 Please help me solve this equation The answer I have is a. i/2 b. -i c. i or d. -i/2 Can you he      Log On


   

Question 174535: Write the expression in the standard form a + bi
(√2/2+√2/2i)^2
Please help me solve this equation
The answer I have is a. i/2 b. -i c. i or d. -i/2
Can you help me? Thank you
Found 2 solutions by jim_thompson5910, Alan3354:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=sqrt%282%29%2F2


So the expression %28sqrt%282%29%2F2%2B%28sqrt%282%29%2F2%29i%29%5E2 becomes %28x%2Bx%2Ai%29%5E2


%28x%2Bx%2Ai%29%5E2 Start with the given expression.


x%5E2%2Bx%5E2%2Ai%2Bx%5E2%2Ai%2Bx%5E2%2Ai%5E2 FOIL


x%5E2%2B2x%5E2%2Ai%2Bx%5E2%2Ai%5E2 Combine like terms.


x%5E2%2B2x%5E2%2Ai%2Bx%5E2%28-1%29 Replace i%5E2 with -1. Remember, i%5E2=-1


x%5E2%2B2x%5E2%2Ai-x%5E2 Multiply


2x%5E2%2Ai Combine like terms.


2%28sqrt%282%29%2F2%29%5E2%2Ai Plug in x=sqrt%282%29%2F2


2%281%2F2%29%2Ai Square sqrt%282%29%2F2 to get


i Multiply



So %28sqrt%282%29%2F2%2B%28sqrt%282%29%2F2%29i%29%5E2=i which means that the answer is c) i


So the answer in standard form a%2Bbi is 0%2B1%2Ai where a=0 and b=1



Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Write the expression in the standard form a + bi
(√2/2+√2/2i)^2
Please help me solve this equation
The answer I have is a. i/2 b. -i c. i or d. -i/2
-------------------
%28%28sqrt%282%29%2F2%29+%2B+sqrt%28-1%29%2A%28sqrt%282%29%2F2%29%29%5E2 I think that's what you meant.
Factor out %28sqrt%282%29%2F2%29%5E2, which is 1/2
= 1%2F2%2A%281+%2B+sqrt%28-1%29%29%5E2
=1%2F2%2A%281+-1+%2B+2sqrt%28-1%29%29
=1%2F2%2A2sqrt%28-1%29
= i