I need to find all the solutions of the equation
.
I know that I can use the quadratic equation and then use a partial result of that to solve for the roots. However, when I use the quadratic equation, I come up with an answer that just doesn't make sense to me, i.e. . I am not sure where to go from here. I have gone over my calculations several times and this is just what I get... I will appreciate your help. (Sorry, I can't remember how to do the plus/minus sign). Thanks.
Actually, you did NOT make an error, you simply have not finished the problem. You want to write the solutions in the "standard" form "a+ bi".
Use the quadratic formula (not "quadratic equation") with a= 1, b= 4i, and c= -4- 2i.
(which is what you got) where I have dropped the " " since I will be using the two roots of 2i.
"2i" is at (0, 2) in the complex plane, 90 degrees from the real axis, so its square roots are at 45 and -45 degrees, still distance 2 from the origin. That is, they are and . The solutions to the equation are
and .
The OP had 4i. (You have -2i !?). If the OP had read my post properly, s/he would have seen that it's 2i. As I said over a day ago, a careless error made by the OP.
However, the OP has marked the thread as solved and Thanked HoI and generally seems perfectly happy to swap one careless error for another, so who am I to rock the boat ....