Category: Complex Numbers and Quadratic Equations

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

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

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

3. Reduce ((frac{1}{1-4i}-frac{2}{1+i})(frac{3-4i}{5+i})) to the standard form. Complex Numbers and Quadratic Equations Miscellaneous Exercise Previous Next Class 11

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)).  Complex Numbers and Quadratic Equations

1. Evalaute: ([i^{18}+(frac{1}{i})^{25}]^3). Complex Numbers and Quadratic Equations Miscellaneous Exercise Previous Next Class 11 Complex Numbers and Quadratic

14. Express the following expression in the form of a + ib: (frac{(3+isqrt5)(3-isqrt5)}{(sqrt3+isqrt2)-(sqrt3-isqrt2)}). Complex Numbers and Quadratic Equations

Find the multiplicative inverse of each of the complex numbers given in the Exercises 11 to 13. 13.

Find the multiplicative inverse of each of the complex numbers given in the Exercises 11 to 13. 12.

Find the multiplicative inverse of each of the complex numbers given in the Exercises 11 to 13. 11.