Consider the complex number **z = a + bi**, of module and argument **.**

We have to:

Replacing in **z = a + bi**we have:

This expression is called **trigonometric form** or **polar** of the complex **z**.

**Example 1**

Write in complex form the complex number **z = 1 + i**:

*Resolution*

**Module:**

**Argument:**

Therefore, **z** can be written in trigonometric form:

**Example 2**

Write in complex form the complex number **z = 8i**:

*Resolution*

**Module:**

**Argument:**

Therefore, **z** can be written in trigonometric form:

**Example 3**

Write in algebraic form the complex number :*Resolution*

This transformation is immediate because it is enough to replace and by their values:

Next: Multiplication and Division in the Trigonometric Form