graph arg(Z+i)-arg(Z-i)=pi/4

Question

amriju · Answer

u can remember hundreds of special cases...but u have a general...but a bit lenghty rule....take z=x+iy....now put it in the eqn....u know that arg( a+ib)=tan^-1(b/a)...use this defination....then solve for tan^-1((y+1)/x)-tan^-1((y-1)/x)=tan^-1(1)...u get the relation betn x and y...thats ur locus...essentially it will be a circle...centre probb...(1,0) with radius 1.4

anonymous · Answer

hey im not really sure how to simplify after the tan^-1 part..

anonymous · Answer

@amriju  help!!

amriju · Answer

u kno the formula...? of $$\tan^{-1} a-\tan^{-1} b$$

anonymous · Answer

noep

anonymous · Answer

how to combine

amriju · Answer

$$\tan^{-1} a-\tan^{-1} b=\tan^{-1} ((a-b)/(1+ab))$$..but u hav to be good in trigo to solve complex numbers...u kno..?

anonymous · Answer

nope.. dont think i've learnt this before

amriju · Answer

u HAVE TO kno dis...else u wont be able to work out problems on arguments

anonymous · Answer

oh.. so cant do other wya?

amriju · Answer

yeah....there  r different cases lyk..." if this is given, the locus will be this..."...learn all of them...

anonymous · Answer

yeah i cant do these.. trouble with arg ones

amriju · Answer

thats coz ur trigo is weak...

anonymous · Answer

how so?? i've never learnt much about the inverse trig functions

amriju · Answer

u betr learn...to solve arg u need it

anonymous · Answer

how do i lear??

anonymous · Answer

can you teach me

amriju · Answer

its a pretty large chapter...u shud look for a maths specialist....