Complex Numbers

JEE Main Mathematics · 8 questions

All questions, latest first

• The number of values of z ∈ C, satisfying the equations |z-(4+8 i)|=√10 and |z-(3+5 i)|+|z-(5+11 i)|=4 √5, is:20268 April, Shift 2 · Q2
• Let S={z ∈ C: z^2+√6 i z-3=0}. Then Σ_z ∈ S z^8 is equal to:20266 April, Shift 2 · Q3
• Let the set of all values of k ∈ R such that the equation z(z̄+2+i)+k(2+3 i)=0, z ∈ C, has at least one solution, be the interval…20266 April, Shift 1 · Q4
• Let z_1, z_2 ∈ C be the distinct solutions of the equation z^2+4 z-(1+12 i)=0. Then |z_1|^2+|z_2|^2 is equal to:20265 April, Shift 2 · Q2
• Let S={z ∈ C: z^2+4 z+16=0}. Then Σ_z ∈ S|z+√3 i|^2 is equal to:20264 April, Shift 2 · Q2
• Let z be a complex number such that |z+2|=|z-2| and ((z+3)/(z-i))=(π)/4. Then |z|^2 is equal to:20264 April, Shift 1 · Q3
• Let the circles C_1:|z|=r and C_2:|z-3-4 i|=5, z ∈ C, be such that C_2 lies within C_1. If z_1 moves on C_1, z_2 moves on C_2 and…20262 April, Shift 2 · Q2
• 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