Algebra of Complex Numbers

JEE Main Mathematics · Complex Numbers · 13 questions, latest first

• Let x and y be real numbers such that 50((2 x)/(1+3 i)-y/(1-2 i))=31+17 i, i=√-1. Then the value of 10(x-3 y) is:20262 April, Shift 1 · Q2
• Let A={θ ∈[0,2 π]: 1+10 Re((2 cos θ+i sin θ)/(cos θ-3 i sin θ))=0}. Then Σ_θ ∈ A θ^2 is equal to20258 April, Shift 2 · Q3
• Let the product of ω_1=(8+i) sin θ+(7+4 i) cos θ and ω_2=(1+8 i) sin θ+(4+7 i) cos θ be α+i β, i=√-1. Let p and q be the maximum…20254 April, Shift 2 · Q3
• The sum of all possible values of θ ∈[-π, 2 π], for which (1+i cos θ)/(1-2 i cos θ) is purely imaginary, is equal to:20248 April, Shift 2 · Q7
• Let z_1 and z_2 be two complex numbers such that z_1+z_2=5 and z_1^3+z_2^3=20+15 i. Then, |z_1^4+z_2^4| equals -202431 January, Shift 2 · Q3
• If α denotes the number of solutions of |1-i|^x=2^x and β=((|z|)/((z))), where z=(π)/4(1+i)^4[(1-√π i)/(√π+i)+(√π-i)/(1+√π i)],…202431 January, Shift 1 · Q22
• If z=1/2-2 i is such that |z+1|=α z+β(1+i), i=√-1 and α, β ∈ R, then α+β is equal to202429 January, Shift 1 · Q3
• If the set {Re((z-z̄+z z̄)/(2-3 z+5 z̄)): z ∈ C, Re(z)=3} is equal to the interval (α, β], then 24(β-α) is equal to202315 April, Shift 1 · Q3
• Let S={z ∈ C-{i, 2 i}: (z^2+8 i z-15)/(z^2-3 i z-2) ∈ R}. If α-13/11 i ∈ S, α ∈ R-{0}, then 242 α^2 is equal to ____.202311 April, Shift 2 · Q21
• Let the complex number z=x+i y be such that (2 z-3 i)/(2 z+i) is purely imaginary. If x+y^2=0, then y^4+y^2-y is equal to:202310 April, Shift 1 · Q2
• Let A={θ ∈(0,2 π): (1+2 i sin θ)/(1-i sin θ). is purely imaginary }. Then the sum of the elements in A is20238 April, Shift 2 · Q2
• Let z=1+i and z_1=(1+i z̄)/(z̄(1-z)+1/z). Then 12/(π) (z_1) is equal to ____.202330 January, Shift 1 · Q82
• For two non-zero complex numbers z_1 and z_2, if Re(z_1 z_2)=0 and Re(z_1+z_2)=0, then which of the following are possible? A.…202329 January, Shift 1 · Q63