Complex Numbers MCQ Test 3

1. Determine the principal value of arccos(-1).

2. Simplify the expression 'i^3'.

3. Calculate the product of the complex numbers (2 + 3i) and (1 + 4i).

4. If z = 3 - 4i, what is the magnitude of z?

5. Find the roots of the equation 'z^4 + 1 = 0' for complex 'z'.

6. If z = -3 + 4i, what is the real part of z?

7. What is the argument of the complex number '10(cos 120° + i sin 120°)'?

8. What is the magnitude of the complex number '9 + 12i'?

9. If z = 4 - 3i, what is the imaginary part of z?

10. Determine the roots of the equation 'z^2 + 2z + 2 = 0' for complex 'z'.

11. What is the magnitude of the complex number '9 - 12i'?

12. Calculate the value of 'tan(iπ/2)'.

13. Calculate the product of the complex numbers (5 + 2i) and (1 - i).

14. Solve the equation 'z^2 + 1 = 0' for complex 'z'.

15. If z = -5 + 12i, what is the argument of z?

16. Express the complex number '-3 - 4i' in polar form.

17. Determine the argument of the complex number '2 + i'.

18. Find the square of the complex number '2 + 5i'.

19. Calculate the product of the complex numbers (2 + i) and (3 - 4i).

20. What is the conjugate of the complex number '2 - 7i'?

21. If z = 5 - 2i, what is the imaginary part of z?

22. Solve the equation 'z^4 = 1' for complex 'z'.

23. What is the argument of the complex number '4 - 4i'?

24. Find the square of the complex number '3 - 2i'.

25. If z = 3 + 4i, what is the imaginary part of z?

26. What is the magnitude of the complex number '5 + 12i'?

27. What is the real part of the complex number '7 + 2i'?

28. Evaluate 'sin(2iπ/3)'.

29. What is the argument of the complex number '12(cos 120° + i sin 120°)'?

30. If z = 2 + 3i, what is the real part of z?