## Vineet Loomba is teaching live on Unacademy Plus

IIT-JEE CRASH COURSE FOR SURE SHOT SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Search vineet loomba unacademy" on GOOGLE IIT-JEE MATHS REVISION COURSE PREPARED BY: ER. VINEET LOOMBA IITiAN | IIT-JEE MENtoR

REVISION COURSE FOR JEE MAIN AND ADVANCED (IIT-JEE ABOUT ME B.Tech. From IIT Roorkee IIT-JEE Mentor Since 2010. Doubts/Feedback/Ideas in Comment Section. Comment other topics you want to revise. Follow me @ https://unacademy.com/user/vineetloomba to get updates. Share among your peers as SHARING is CARING !!

COMPLEx NUMBERS FOR SURE SHOT SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) #MODULUS AND ARGUMENT IIT-IEE MATHS REVISION COURSE PREPARED BY: ER. VINEET LOOMBA IITiAN | IIT-JEE MENTOR

REVISION COURSE FOR JEE MAIN AND ADVANCED (IIT-JEE MoDULUS OF A COMPLEX NUMBER The modulus, which can be interchangeably represented by orr, is the distance of the pointz from the orign, sothat its numerical value isgiven by _r_Vr'T MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)

REVISION COURSE FOR JEE MAIN AND ADVANCED (IIT-JEE Example: Find the complex numbers zwhich simultaneously satisfy the equations Solution: z-125 z-4 z-8i3 z-8 x-4+iy Here z-125 x=012-sil-3 -25y +136-0 9(364 y*)-2536 + (y-8 y = 17, 8 Hence the required numbers are z = 6 + 1 71 6 + 8 i. MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)

REVISION COURSE FOR JEE MAIN AND ADVANCED (IIT-JEE PRINCIPAL ARGUMENT OF A CoMPLEX NuMBER 2 z lies in the first quadrant z lies in the second quadrant MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)

REVISION COURSE FOR JEE MAIN AND ADVANCED (IIT-JEE PRINCIPAL ARGUMENT OF A CoMPLEX NuMBER z lies in the third quadrant 2 lies in the fourth quadrant 2 MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)

REVISION COURSE FOR JEE MAIN AND ADVANCED (IIT-JEE Method of finding the principal value of the argument ofa complex number z = x + y. Step 1 : Find tan and this gives the value of in the first quadrant. StepII: Find the quadrant in which z lies, with the help ofsign of x and y coordinates. MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)

REVISION COURSE FOR JEE MAIN AND ADVANCED (IIT-JEE b> 0, then + b > 0, then (i) If z lies in the I quadrant principal argument-6- and general argument-2 k If z lies in the II quadrant principal argument-6-7- and general argument-2 If z lies in the III quadrant principal argument-0- + and general argument-2 k + ( - ) If z lies in the IV quadrant principal argument-0- and general argument-2 k- i.e. a >0 and (ii) i.e. a < 0 and + ( - ) (iii) i.e. a < 0 and b< 0, then (iv) i.e. a> 0 and b < 0, then MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKee)

REVISION COURSE FOR JEE MAIN AND ADVANCED (IIT-JEE POLAR FORM z r (cos + i sin ) EULeR FORM z=re =cos + i sin MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)

REVISION COURSE FOR JEE MAIN AND ADVANCED (IIT-JEE PROPERTIES arg (zi . Z2 3 z") = arg (zi) + arg (z,) + + arg (z.) 2.121-211 arg()=arg (zi )-arg (:) . 4 MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)

REVISION COURSE FOR JEE MAIN AND ADVANCED (IIT-JEE Example: If z-2il 2, then find the greatest and least of z Solution: we have lz _ 2 + il -12-11-11 -,51 Hence greatest value of lis 5 + 2 and least value of lis 5-2. MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)