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Trigonometric or polar shape


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

We have to:

Replacing in z = a + biwe 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