Trigonometry : Complex Numbers

Study concepts, example questions & explanations for Trigonometry

varsity tutors app store varsity tutors android store

Example Questions

Example Question #26 : Complex Numbers/Polar Form

The following graph represents which one of the following?


Screen shot 2020 08 04 at 1.05.05 pm

Possible Answers:

Correct answer:

Explanation:

The above image is a graphic representation of subtraction of complex numbers (which are represented by vectors  and . We can take any complex number  and graph it as a vector, measuring  units in the x direction and  units in the y direction. Therefore . Likewise, .

To help us visualize subtraction, instead of thinking about taking , we should instead visualize . The below figure shows  with a dotted line. Visually, the resultant vector  lies in between the vectors  and . Algebraically, we get   or  . Either way you think about it, the resulting vector is 

 

Screen shot 2020 08 04 at 1.05.55 pm

Learning Tools by Varsity Tutors