13. If (a + ib) (c + id) (e + if) (g + ih) = A + iB, then show that (a² + b²) (c² + d²) (e² + f²) (g² + h²) = A² + B². Complex Numbers and Quadratic…
12. Find the number of non-zero integral solutions of the equation (|1-i|^x=2^x). Complex Numbers and Quadratic Equations Miscellaneous Exercise Previous Next Class 11 Complex Numbers and Quadratic Equations Miscellaneous Exercise 1. Evalaute: ([i^{18}+(frac{1}{i})^{25}]^3). 2. For any two complex numbers (z_1) and (z_2),…
11. If α and β different complex numbers with |β|=1, then find (|frac{β-α}{1-bar{α}β}|) Complex Numbers and Quadratic Equations Miscellaneous Exercise Previous Next Class 11 Complex Numbers and Quadratic Equations Miscellaneous Exercise 1. Evalaute: ([i^{18}+(frac{1}{i})^{25}]^3). 2. For any two complex numbers (z_1) and…
10. If ((x+iy)^3=u+iv), then show that (frac{u}{x}+frac{v}{y}=4(x^2-y^2)). Complex Numbers and Quadratic Equations Miscellaneous Exercise Previous Next Class 11 Complex Numbers and Quadratic Equations Miscellaneous Exercise 1. Evalaute: ([i^{18}+(frac{1}{i})^{25}]^3). 2. For any two complex numbers (z_1) and (z_2), prove that (Re(z_1 z_2)=Re(z_1)Re (z_2))(-Im(z_1)Im(z_2)). …
9. Find the modulus of (frac{1+i}{1-i}-frac{1-i}{1+i}). Complex Numbers and Quadratic Equations Miscellaneous Exercise Previous Next Class 11 Complex Numbers and Quadratic Equations Miscellaneous Exercise 1. Evalaute: ([i^{18}+(frac{1}{i})^{25}]^3). 2. For any two complex numbers (z_1) and (z_2), prove that (Re(z_1 z_2)=Re(z_1)Re (z_2))(-Im(z_1)Im(z_2)). 3.…
8. Find the real numbers x and y if (x – iy) (3 + 5i) is the conjugate of –6 – 24i. Complex Numbers and Quadratic Equations Miscellaneous Exercise Previous Next Class 11 Complex Numbers and Quadratic Equations Miscellaneous Exercise 1.…
7. Let (z_1=2-i, z_2=-2+i). Find (i) (Re(frac{z_1 z_2}{bar{z_1}})) (ii) (Im(frac{1}{z_1 bar{z_1}})) Complex Numbers and Quadratic Equations Miscellaneous Exercise Previous Next Class 11 Complex Numbers and Quadratic Equations Miscellaneous Exercise 1. Evalaute: ([i^{18}+(frac{1}{i})^{25}]^3). 2. For any two complex numbers (z_1) and (z_2), prove…
6. If (a+ib=frac{(x+i)^2}{2x^2+1}), prove that (a^2+b^2=frac{(x^2+1)^2}{(2x^2+1)^2}). Complex Numbers and Quadratic Equations Miscellaneous Exercise Previous Next Class 11 Complex Numbers and Quadratic Equations Miscellaneous Exercise 1. Evalaute: ([i^{18}+(frac{1}{i})^{25}]^3). 2. For any two complex numbers (z_1) and (z_2), prove that (Re(z_1 z_2)=Re(z_1)Re (z_2))(-Im(z_1)Im(z_2)). 3.…
5. If (z_1=2-i, z_2=1+i), find (|frac{z_1+z_2+1}{z_1-z_2+1}|). Complex Numbers and Quadratic Equations Miscellaneous Exercise Previous Next Class 11 Complex Numbers and Quadratic Equations Miscellaneous Exercise 1. Evalaute: ([i^{18}+(frac{1}{i})^{25}]^3). 2. For any two complex numbers (z_1) and (z_2), prove that (Re(z_1 z_2)=Re(z_1)Re (z_2))(-Im(z_1)Im(z_2)). 3.…
4. If (x-iy=sqrt{frac{a-ib}{c-id}}), prove that ((x^2+y^2)^2=frac{a^2+b^2}{c^2+d^2}). Complex Numbers and Quadratic Equations Miscellaneous Exercise Previous Next Class 11 Complex Numbers and Quadratic Equations Miscellaneous Exercise 1. Evalaute: ([i^{18}+(frac{1}{i})^{25}]^3). 2. For any two complex numbers (z_1) and (z_2), prove that (Re(z_1 z_2)=Re(z_1)Re (z_2))(-Im(z_1)Im(z_2)). 3.…
