complex q (1 Viewer)

[kkk579]

how do you know when to use +kpi or +2kpi? for example, a q where it asks you to find what values cis(2theta) is imaginary for. you would let cos2theta =0 and then would get 2theta=0+k2pi or kpi right? but how do you know which one to use each time because different sols use kpi and others use 2kpi so im js rlly confused

 

[Scrambled]

how do you know when to use +kpi or +2kpi? for example, a q where it asks you to find what values cis(2theta) is imaginary for. you would let cos2theta =0 and then would get 2theta=0+k2pi or kpi right? but how do you know which one to use each time because different sols use kpi and others use 2kpi so im js rlly confused

oh they're both technically right I think it just depends on how you look at it that's all
If you think of a cos graph between 0 and 2pi, cosx = 0 when x = pi/2, 3pi/2. Now you can either do x = (pi/2 + 2kpi), (3pi/2 +2kpi), or you can just simplify it as x = pi/2 + kpi as 3pi/2 is just pi/2 + pi. Same thing applies for sin, where you can either write it as x= (0 + 2kpi), (pi + 2kpi) or as x =0 + kpi = pi

Basically you're always going to use 2kpi for all the solutions between 0 and 2pi, but you can simplify it further because the intercepts for sin and cos are just +- pi apart

idk my explanation was probably really bad someone else help me

 

[liamkk112]

how do you know when to use +kpi or +2kpi? for example, a q where it asks you to find what values cis(2theta) is imaginary for. you would let cos2theta =0 and then would get 2theta=0+k2pi or kpi right? but how do you know which one to use each time because different sols use kpi and others use 2kpi so im js rlly confused

depends
if you're solving cosx = 0, then the solutions will be pi/2, 3pi/2, etc right, so everything differs by pi
but if you're solving cosx = 1, then the solutions will be 0, 2pi, etc
0 is a special case where the solutions differ by pi, but in general for any other number, solutions to a trig function like cosx or sinx will be 2pi periodic

 

[C2H6O]

how do you know when to use +kpi or +2kpi? for example, a q where it asks you to find what values cis(2theta) is imaginary for. you would let cos2theta =0 and then would get 2theta=0+k2pi or kpi right? but how do you know which one to use each time because different sols use kpi and others use 2kpi so im js rlly confused

I'm guessing you're talking more about solving these trig problems rather than complex questions? Cause the only time you really see kpi in purely complex number questions is in roots of unity. In this case you'd probably want to know the general solutions for trig equations:



Yes this is out of syllabus and you don't have to memorise it but my teacher taught it anyway and I find it really helpful. I hope I'm not confusing you here, but essentially you can apply these solutions to any trig problem and it can find all solutions. Unfortunately for most of these trig questions it isn't as straightforward as +kpi or +2kpi except for tan which is periodic by pi. To solve your problem we have