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Lesson: Finding the Argument of a Complex Number

In this lesson, we will learn how to identify the argument of a complex number and how to calculate it.

Worksheet • 12 Questions

Q1:

A complex number is multiplied by another complex number 𝑧 , and then by the complex conjugate 𝑧 βˆ— . How is the argument of the original complex number affected?

  • AIt is unchanged.
  • BIt is increased by the argument of 𝑧 βˆ— .
  • CIt is increased by twice the argument of 𝑧 .
  • DIt is increased by πœ‹ .
  • EIt is increased by twice the argument of 𝑧 βˆ— .

Q2:

Consider the complex number 𝑧 = 7 + 7 𝑖 .

Find the argument of 𝑧 .

  • A πœ‹ 4
  • B πœ‹ 2
  • C 7 √ 2
  • D7
  • E 3 πœ‹ 4

Hence, find the argument of 𝑧 4 .

  • A πœ‹
  • B πœ‹ 4
  • C ο€» πœ‹ 4  4
  • D 2 πœ‹
  • E πœ‹ 1 6

Q3:

Given that principal argument ( 𝑍 ) = 5 πœ‹ 6 , determine principal argument ο€Ή 𝑍  2 .

  • A βˆ’ πœ‹ 3
  • B βˆ’ 2 πœ‹ 3
  • C πœ‹ 3
  • D βˆ’ πœ‹ 6
  • E πœ‹ 6
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