Complex Numbers and Quadratic Equations

JEE Main 2024 (Online) 29th January Evening ShiftNumericalMedium📈 Topic in 16% papers+4

Ques. 1JEE Main 2024, 29 January (Evening Shift)

Let , be the roots of the equation x2- 6x+3=0 such that Im( )>Im( ). Let a, b be integers not divisible by 3 and n be a natural number such that 99 + 98=3n(a+ib), i= -1. Then n+a+b is equal to .

Answer

Solution

x= 6 i 62 = 3 ei /4, = 3 e-i /4

99 + 98= 98 +

98=349ei 49 /2=349 i

+ = 6 3 e-i /4= 2 ei /4=1+i

349 i(1+i)=349(-1+i) n=49, a=-1, b=1

n+a+b=49

Answer: 49

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Ques. 2JEE Main 2024, 27 January (Morning Shift)

If S=\z :|z-i|=|z+i|=|z-1|\, then, n(S) is :

Ques. 3JEE Main 2024, 27 January (Morning Shift)

If satisfies the equation x2+x+1=0 and (1+ )7=A+B +C 2, A, B, C 0, then 5(3A-2B-C) is equal to .

Ques. 4JEE Main 2024, 27 January (Evening Shift)

If , are the roots of the equation, x2-x-1=0 and Sn=2023 n+2024 n, then :

2S12=S11+S10
S12=S11+S10
S11=S10+S12
2S11=S12+S10

Ques. 5JEE Main 2024, 27 January (Evening Shift)

Let the complex numbers and 1 lie on the circles |z-z0 |2=4 and |z-z0 |2=16 respectively, where z0=1+i. Then, the value of 100| |2 is .

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