Free Printable Properties of Complex Numbers

1.

If $z_1$ and $z_2$ are any two complex numbers, then arg( $z_1$ . $z_2$ ) =

a)

$\arg\left(z_1\right).\arg\left(z_2\right)$

b)

$\arg\left(z_1\right)-\arg\left(z_2\right)$

c)

$\arg\left(z_1\right)+\arg\left(z_2\right)$

d)

$\frac{\arg\left(z_1\right)}{\arg\left(z_2\right)}$

2.

a)

True

b)

False

3.

If z is any complex number, then $z.\overline{z}=$

a)

$z^2$

b)

0

c)

$\left|z\right|^2$

d)

Re(z)

4.

If z = 5, then arg(z) =

a)

$0^c$

b)

$\frac{\pi^c}{2}^{ }$

c)

$\pi^c$

d)

$5^c$

5.

For any two complex numbers, $z_1$ and $z_2$ ,Which of the following is not true?

a)

$\left|z_1+z_2^{ }\right|^2=\left|z_1\right|^2+\left|z_2\right|^2+2Re\left(z_1.\overline{z_2}\right)$

b)

$\left|z_1+z_2^{ }\right|^2=\left|z_1\right|^2+\left|z_2\right|^2+2Re\left(z_1.z_2\right)$

c)

d)

6.

If z = a + ib, where a < 0 and b < 0, then which of the following is correct ?

a)

$0<\arg z<\frac{\pi}{2}$

b)

$\frac{\pi}{2}<\ \arg z\ <\ \pi$

c)

$\pi\ <\ \arg z\ <\ \frac{3\pi}{2}$

d)

$\frac{3\pi}{2}<\arg z\ <2\pi$

7.

If z = a, where $a\in R$ , then $\overline{z}=$

a)

$-a$

b)

$a$

c)

$ai$

d)

$-ai$

8.

If $z_1=3+4i$ and $z_2=12+5i$ , then $\left|z_1.z_2\right|=$

a)

65

b)

18

c)

8

d)

None of the above is correct

9.

For any there complex numbers $z_1$ , $z_2$ and $z_3$ , the property $z_1.\left(z_2+z_3\right)=z_1.z_2+z_1.z_3$ is known as

a)

Associative property

b)

Commutative property

c)

Closure Property

d)

Distributive Property

10.

The geometrical representation of a complex number in a complex plane is called as

a)

Argand's Diagram

b)

Euler's Diagram

c)

Napier's Diagram

d)

Euclid Diagram

Properties of Complex Numbers

Total questions: 10

Worksheet time: 5mins

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