Question 204916: Q.1. Find the fourth roots of -1.
Q.2. If 3/(2+cosx + isinx )=a+ib,then prove that a.a+b.b =4a-3.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Q.1. Find the fourth roots of -1.
-1 = -1+0i corresponds to the point (-1,0)
---
r = sqrt(1^2+0^2) = 1
theta = tan^-1(0/-1) = 180 degrees
-------------
So: -1 = 1(cos(180+360n) + isin(180+360n)
And (-1)^(1/4) = (1)^1/4(cos(180+360n)/4 + isin(180+360n)/4)
------
Let n= 0 then (-1)^(1/4) = 1(cos(45) + isin(45))
---
Let n = 1 then (-1)^(1/4) = 1(cos(135)+isin(135))
---
Let n = 2 then (-1)^(1/4) = 1(cos(225)+ isin(225))
---
Let n = 3 then (-1)^(1/4) = 1(cos(315)+isin(315))
=================================================
Cheers,
Stan H.
=================================================
Q.2. If 3/(2+cosx + isinx )=a+ib,then prove that a.a+b.b =4a-3.
Prove what?
===================
Cheers,
Stan H.
|
|
|
