JEE Advanced 2021 | Complex Numbers easy question solved by 18,000 JEE Aspirants, Can you?

[@TheJugx]

just find the intersection of circle and x axis put y=0 x^2+5x+4=0 -4 and -1 will be the roots and while writing it in argument it will be +1 and +4 and by some logic i easily figured whats alpha and beta

[@dnyaneshkadu2362]

Please make a video on jee adv 2018's toughest question of circle

[@vacationspecial3151]

Yes!

[@adityaatiitg]

normal people are solving by these methods but toppers just putting y=0 and find roots of quadratic

[@rationale1734]

Nice

[@TheJugx]

nah they aint topper (i did the same and im not topper lmao)

[@adityaatiitg]

@@TheJugx if you solved it by yourself then you will become very soon

[@khuranapranshu]

y=0 se kaise aayega ??

[@adityaatiitg]

​@@khuranapranshuBecause alpha, beta are real and lie on that circle So their imaginary part will be zero

[@nihal6783]

My method was : Arg((x+a) +iy) /(x+B) +iy)=π/4 Then i multiplied numerator and denominator inside argument by the quantity which is present in denominator and hence we end up with the equation : Tan^-1((x^2+y^2+(a+B)x+aB+(B-a)yi)/(x^2+B^2+2Bx+y^2)) = π/4 Then split the numerator into two parts such that it forms the complex number : tan^-1((x^2+y^2+(a+B)x+aB)/(x^2+B^2+2Bx+y^2)) + ((B-a)y/(x^2+B^2+2Bx+y^2)))i) = π/4 Now as we know that argument of any complex number w=c+id is d/c So, the argument of above equation will be : (B-a)y / x^2+y^2+(a+B)x+aB = tan (π/4) =1 then cross multiply the terms and take all the terms to right hand side making left hand side zero. And the equation will be : x^2+y^2+(a+B)x-(B-a)y+aB=0 And by comparing above equation with equation of circle we will get two options correct : B and D

[@NoName069]

Arey bhai 😅

[@rationale1734]

Bhaiya arc ki eqn lag....Pythagoras se eqn a gyi

[@rawatutkarsh]

Pretty easy question bhaiya Solved it by 1st method under 3 minutes

[@sakshamsingh1778]

😂😂🤡

[@rawatutkarsh]

@@sakshamsingh1778 kya be

[@krishgarg2806]

I did a mix of 2 and simpler approach. as alpha and beta are real, and they will be in the locus circle of z, I just put y = 0 in the circle eqn. from here we get -1 and -4. now the 2nd approach part, we know these will be -alpha and -beta, hence we get alpha beta = 1 and 4 deciding which is which, we can check using clockwise and anticlockwise rotations to see -alpha > -beta, hence alpha < beta we get alpha = 1, beta = 4 this looks lengthy but I was able to solve like this under a minute.

[@ujjwalsinghpal8220]

Bro ye kese pta chala ki alpha beta locus pr h

[@krishgarg2806]

@@ujjwalsinghpal8220 again rotation ke idea se, locus arc hoega with -alpha and -beta as end points of the arc. technically unhe include nhi karenge, but poora circle de rkha hai to usme included hoga hi

[@annapurnasarangi9999]

I did 2 appr, 1 is coni method, and another one was radius equal.. in the 2nd method I got 2 values for a and B, but then I saw the options, and got tk that alpha and beta should be positive, then possible values are 1 and 4, then as both of them won't be the same, I got beta will 4

[@apratimtewari4288]

rotation wale se sirf ye realise hojaye ki arg(z+a/z+b)= pi/4 represents major arc of circle. Eqn of circle is given. Also alpha and beta given as real so they are points where x^2+y^2+5x-3y+4=0 cuts x axis. Option se alpha aur beta ki values daalke dekhlo ya y=0 put kr quadratic solve karlo hogaya solve question.

[@chiragsharma4968]

aaj hi rotation seekha tha, hogya...accha laga solve krke😅

[@raytheboss4650]

for method 2 z should be -5/2 +3i/2 and z+alpha = i(z+beta)

[@phantom_iitBHU]

Just put x= iy and multiply conjugate of denominator on both numerator and den. Equating real and imaginary parts and comparing with the equation we easily get the values of alpha beta

[@Mindblo]

A more easy way would be just funding x intercepts of circle which will be alpha and beta it's will also come -1 and -4

[@anjuomji]

Meko ese question ni hota but solution dekhta hu to lagta h ki ye etna asan tha mere dimag me kiyu ni aya ye 😢kya kru?

[@offroadgamer9705]

Solve karr bass aur kuch option nahi haii

[@LokeshSuryawanshi264]

Tum akele nahi ho 😅

[@droyprimechoudhary1802]

Bhai summary banao sab chapters ka tabhi sab concepts yaad rahege.Nahi to yehi sab hoga.

[@LegendaryBea]

Course lele set of 60 😂

[@rahulmaravii]

Same😊

[@JohnDoe-hl2qm]

π/4 angle dekhte hi, *real part=imaginary part* [after simplifying, rationalising denominator]

[@jagruknagrik0517]

Done it with second approach , alpha beta me perpendicular lines ka slope wala lagake kardiyan❤❤❤

[@annapurnasarangi9999]

Bhaiya the conplex number for the centre shouldnt it be -5/2 + 3/2i ? And also, the coni method, it should be z+a = i(z+B)

[@team_0718]

Bhaiya mujhe confidence mai provlem hori mujhe adhe simplification mai lagta hai ki galat hora hai par voh sahi hota he😢

[@yatharth2463]

Was expecting you to use rotation, easily hojate h aise ques usse

[@satvikyadav7469]

Finally first time mera koi question under 2 min hua thanku bhaiya(advance question)

[@sakshamsingh1778]

(Please do not delete my comment) 2:12 pe aapne jo likha hai na ki argument of a complex number a+ib is tan inv b/a This is not always true Let's say -1-i ek complex number hai ye third quadrant me kahi hai par iska tan inv (-1/-1) kroge na to wo π/4 aata h indicating that this thing is not true. So your first solution is not quite rigorous

[@krishgarg2806]

well it is also true that the entire circle is not the locus of z. only part of the circle. as we are looking for more general possible locus, it is a fair lead to go with just tan-1

[@Ayush-yj5qv]

We can assume and solve rigorously also it's not very hard

[@srikarm985]

Maine is paper ko as a mock diya tha pichle Sunday ko, and karte time is equation mein substitute karke solve karne ka try kiya but hua nhi. Uske baad expand karne ka socha, in the way you did, but time nhi bacha...

[@ignonane]

SIR easy sawaal tha😂❤

[@Raj-xt4fk]

Its not said that a and b lie on that circle. So how will rotation method work?

[@mryash2565]

Standard question hai saare teachers kara dete hai ye wala

[@adityajha2889]

103 seconds Method:- argument ke andar hi denominator k conjugate se upar nihe multiply karo Denominator me jo bhi aaye(kyoki wo numerator k real aur imaginary part k liye common hoga) But numerator me jo aega uska real aur imaginary barabar krke ek circle bana lo fir compare krdo 103 seconds bhi isliye lag gye kyoki stopwatch mil nhi rhi thi😂

[@Shivang8545]

Bhaiya isko arc Wale se bhi kr skte h -alpha aur -beta uss given circle PR lie krenge aur dono real h toh dono ka imaginary part 0 krke alpha aur beta nikal skte h itna calculation bhi ni krna padega

[@anwita5]

Sir can u tell in 5:46 ,how 2+beta ,answer is not coming?

[@adityajha2889]

Z likhna chahte the bhai Mujhe ye batao ki z =-5/2+3/2i hona chahiye na

[@anwita5]

Yes ,you are right ,

[@jodplays3425]

Bhaiya Maine 11th Ka Syllabus Khatam Krliya Mere Teacher ne To Ye Brute Force Method nhi sikhaya Tan-¹ wala

[@itzSiddhxrth]

School mein nhi sikhate bhai ye sab. Jee ke coaching mein sikhaya jaata he

[@temporaryname9914]

complex number skip kar sakte hai kya??

[@Bald114]

Since a and B are real cant we just put y=0 and solve the quadratic ??

[@naitikagarwal9654]

Merko toh keval second wala hi aata hai ... Kafi easy ho jata hai rotation se every question

[@prahladkumar7120]

bhaiya aise hi physics aur chemistry ke questions daala karo

[@AryanKatiyar289]

2-2:30min observe krne me aur 30 sec solve krne me graphical method se

[@PranavSinghJEE2025]

Bhaiya rotation se krne me question todha lamba jyega but comparitively easy hoga 😅

[@anshverma8509]

Hlo uncle👋 thnx...

[@shaatirop8901]

Thank you rotation revise ho gya

[@anuragsengupta9269]

Got it right 👍

[@LEGEND_SPRYZEN]

Ezy qs bhaiya

[@abhinavbhutada2991]

Ok SIR 😂

[@surajj303]

Bhaiya main ye rotation se kiya tha❤

[@priyanshichauhan3409]

thanks bhaiya

[@Ayush-yj5qv]

Rotation se kiya 🛐

[@Discodeewane72]

Rotation se kara bhaiya

[@jeesimplified-subject]

Good work brother

[@Discodeewane72]

Thank you 👍

[@vijendrashelawadi3990]

Bhaiya faked us

[@shaatirop8901]

B D