Complex Number and Quadratic Equations Test Online MCQs

1. The least positive integer n which will reduce (1 + i/1 - i)ⁿ to unity is:

2. The complex number sin x + i cos 2x and cos x - i sin 2x are conjugate to each other for

3. The number of solutions of the equation |x²| - 3 |x| + 2 = 0 is

4. 1 + i² + i⁴ + i⁶ + ....... + i²ⁿ is

5. The coefficient of x in the equation x² + px + q = 0 was taken as 17 in place of 13 and its roots we found to be -2 and -15. The roots of the original equation are

6. Both roots of the equation
(x - b)(x - c) + (x - a)(x - c) + (x -a) (x - b) = 0

7. If Z(3 + 4i) = 2 + 3i then the value of Z is:

8. The argument of (1 - i √3)/(1 + i √3) is

9. If (1 + i)x - 2i/3 + i  +  (2 - 3i)y + i/3 - i = i, then the real values of x and y given by

10. If one root of 5x² + 13x + k = 0 is reciprocal of the other, then k is equal to

11. If 3 + 4i is the root of the equation
x² + px + q = 0, then

12. The value of p for which the difference between the roots of the equation x² + px + 8 = 0 is 2 are

13. If (x + iy)^1/3 = a + ib, then x/a + y/b =

14. The equation x - 2/(x - 1) = 1 - 2/x(x - 1) has

15. The real roots of the equation x² + 5 |x| + 4 = 0 are