Complex Numbers MCQs: The power of iota(i)

1. What is a complex number?
A) A number with both real and imaginary parts
B) A number that consists iota
C) A number that cant be mathematically represented
D) both A and B

2. How complex numbers can be represented?
A) a+ bi
B) eiθ
C) a× bi
D) All

3. How imaginary part of the complex numbers is denoted?
A) e
B) i
C) i²
D) i_n

4.” In a+ bi“, identify real and imaginary parts.
A) a is an imaginary part
B) b is the imaginary part
C) there is no real part
D) a is the real part and b is an imaginary part

5. How does Euler’s formula relate complex exponentials to trigonometric functions?
A) eiθ=cos(θ)+i sin(θ)
B) eiθ=sin(θ)+i cos(θ)
C) eiθ=tan(θ)+i cot(θ)
D) eiθ=sec(θ)+i csc(θ)

6. What is the value of i, iota?
A) sqrt(-1)
B) -1
C) 0
D) 1/3

7. What is the value of i²?
A) -1
B) 0
C) can’t be determined
D) It depends on the problem

8. Solve the equation for z, z² +4=0.
A) z=2i
B) z=-2i
C) z=2,-2
D) z=2i,-2i

9. If z=4+2i, find the complex conjugate of z
A) z=4+2i
B) z=-4+2i
C) z=-4-2i
D) z=4-2i

10. What is the sum of 3+2i and 1-6i?
A) 5+2i
B) 1-2i
C) 4+4i
D) 4-4i

11. If a+bi=3+4i, what is the value of a-b?
A) 1
B) -1
C) 3
D) 6

12. Find the value of z, 2z+1=0.
A) z=1/2
B) z=-1/2i
C)z=-i
D) i/2

13. Find the cube roots of z = −8.
A) 0
B) 1/3
C) -2
D) 2

14. Identify the real and imaginary parts of z=(4-i)/(1-2i).
A) Re(z)=4, Im(z)=2
B) Re(z)=-4, Im(z)=2
C) Re(z)=-4, Im(z)=1/2
D) Re(z)=6/5,Im(z)=7/5