Complex Number : Exercise 1

Introduction
In Exercise 1, basic concepts of complex number are highlighted including

• Simplification of $i^n$
• complex conjugate
• Algebra operations in complex number - Addition, Subtraction, Multiplication, Division and Equality

1. Express each of the following complex numbers in the form of a + bi.









2. Simplify each of the followings.










3. Simplify each of the following by addition or subtraction.









4. Simplify each of the followings.













5. Given that express in the form of a+ bi.








6. Given that $z=-2+i$, express $z+\frac{1}{z}$ in the form of a+ bi. 


7. Given that $z=2-3i$, express $\frac{z}{1-z^2}$ in the form of a+ bi.