## Chapter 13 – Complex Numbers Exercise Ex. 13.1

Find the values of the following expressions:

(1 + i)^{6} + (1 – i)^{3}

## Chapter 13 – Complex Numbers Exercise Ex. 13.2

Evaluate the following :

What is the smallest positive integer n for which

(1+i)^{2n} = (1-i)^{2n}?

If z_{1}, z_{2}, z_{3} are

complex numbers such that |z_{1}| = |z_{2}| = |z_{3}|

= = 1, then

find the value of |z_{1} + z_{2} + z_{3}|.

Find the number of solutions of z^{2} + |z|^{2}

= 0

## Chapter 13 – Complex Numbers Exercise Ex. 13.3

Find the square root of the following complex numbers: -i

## Chapter 13 – Complex Numbers Exercise Ex. 13.4

Write (i^{25})^{3} in polar form.

Express the following complex numbers in the form

r(cos q + I sin q): 1 + i tan a

Express the following complex numbers in the form

r(cos q + I sin q): tan a – i

Express the following complex numbers in the form

r (cos q + I sin q): 1 – sin a + i cos a

Express the following complex numbers in the form

r (cos q + I sin q):