MCQs Number System 3

1. The additive identity in set of complex number is

(1, 0)

(0, 0)

(0, 1)

(1, 1)

2. If $a+ib$ is complex number then its conjugate is

$a=c$ and $b=d$

$ad=bc$

$a=-c$ and $b=d$

$a=d$ and $b=c$

3. If $a+ib$ is a complex number then its conjugate is

$ab$

$\sqrt{a^2+b^2}$

$-a-ib$

$a-ib$

4. The factors of $3(x^2+y^2)$ are

$3(x+y)(x-y)$

$3(x+iy)(x-iy)$

$\sqrt{3}(x+iy)(x-iy)$

None of these options

5. $(0, 1)^4$ is equal to

$i$

$-1$

$1$

$-i$

6. $(-i)^{19}$ is equal to

$-1$

$i$

$-i$

$1$

7. If $z$ is any real number then its conjugate is

A real number

Zero

Any integer

Complex number

8. $(0, 1)^3$ is equal to

$1$

$i$

$-i$

$-1$

9. If $k$ is any real number and $a+ib$ is a complex number then

$|k(a+ib)|=ka-ikb$

$|k(a+ib)| = \sqrt{k^2(a^2+b^2)} $

$|k(a+ib)|=ka+ib$

None of these options

10. (0, 1) is equal to

$1$

$-i$

$i$

$0$

11. $(0, 1)^2$ is equal to

$-1$

$i$

$-i$

$1$

12. The sum of two conjugate complex numbers is

Real or imaginary number

Not defined

A real number

An imaginary number

13. The multiplicative inverse of $(-4, 7)$ is

$(\frac{4}{\sqrt{65}}, \frac{-7}{\sqrt{65}})$

$(\frac{-4}{65}, \frac{-7}{65})$

$(\frac{-4}{\sqrt{65}}, \frac{-7}{\sqrt{65}})$

$(\frac{4}{65}, \frac{-7}{65})$

14. The product of two conjugate complex numbers is

A real number

Maybe an irrational number

Not defined

An imaginary number

15. $(-1)^{-\frac{21}{2}}$ is equal to

$-i$

$-1$

$i$

$1$

16. (0, 3) (0, 5) is equal to

$8i$

$-8i$

$15$

$-15$

17. The additive inverse of $(a, -b)$ is

$(-a, b)$

$(a, b)$

$(-a, -b)$

$(a, -b)$

18. The real part of $\frac{2+i}{i}$ is equal to

$-1$

$\frac{1}{2}$

$2$

$1$

19. The multiplicative inverse of $(a, -b)$ is

$\left(\frac{a}{a^2+b^2}, \frac{-b}{a^2+b^2} \right)$

$\left(\frac{-a}{a^2+b^2}, \frac{b}{a^2+b^2} \right)$

$\left(\frac{a}{\sqrt{a^2+b^2}}, \frac{-b}{\sqrt{a^2+b^2}} \right)$

$\left(\frac{a}{a^2+b^2}, \frac{b}{a^2+b^2} \right)$

20. The multiplicative identity of a complex number is

(1, 1)

(0, 1)

(1, 0)

(0, 0)

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