SOLUTION: Hello =) I really need help with this problem! If you could help me out that would be great! DIRECTIONS: write the complex number is standard form {{{ (sqrt (2) / 2 + (sqr

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Hello =) I really need help with this problem! If you could help me out that would be great! DIRECTIONS: write the complex number is standard form {{{ (sqrt (2) / 2 + (sqr      Log On


   

Question 158029This question is from textbook
: Hello =)
I really need help with this problem! If you could help me out that would be great!
DIRECTIONS: write the complex number is standard form
+%28sqrt+%282%29+%2F+2+%2B+%28sqrt+%282%29+%2F+2%29+i+%29%5E4+
I hope i wrote that right. It's the quantity the squareroot of 2 over 2 plus the squareroot of 2 over 2 times i to the 4th power. I know how to solve it I think but I dont know how to put it in standard form??
Help me out please! Thank you!!! This question is from textbook

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming that you are in a trig class, and that you have the unit circle with you. Looking at the unit circle, we see that cos%28pi%2F4%29=sqrt%282%29%2F2 and sin%28pi%2F4%29=sqrt%282%29%2F2



+%28sqrt+%282%29+%2F+2+%2B+%28sqrt+%282%29+%2F+2%29+i+%29%5E4+ Start with the given expression


+%28cos%28pi%2F4%29+%2B+sin%28pi%2F4%29+i+%29%5E4+ Replace sqrt%282%29%2F2 with cos%28pi%2F4%29 and sin%28pi%2F4%29


+cos%284%28pi%2F4%29%29+%2B+sin%284%28pi%2F4%29%29+i+ Use De Moivre's Theorem to expand


+cos%28pi%29+%2B+sin%28pi%29+i+ Multiply


-1%2B0%2Ai Take the cosine of pi to get -1 and take the sine of pi to get 0


-1 Simplify


So +%28sqrt+%282%29+%2F+2+%2B+%28sqrt+%282%29+%2F+2%29+i+%29%5E4=-1+


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