Angle and absolute value of complex numbers

Everything You Need in One Place

Homework problems? Exam preparation? Trying to grasp a concept or just brushing up the basics? Our extensive help & practice library have got you covered.

Learn and Practice With Ease

Our proven video lessons ease you through problems quickly, and you get tonnes of friendly practice on questions that trip students up on tests and finals.

Instant and Unlimited Help

Our personalized learning platform enables you to instantly find the exact walkthrough to your specific type of question. Activate unlimited help now!

0/5
?
Examples
Lessons
  1. Given the complex number z=2+3iz=2+3i
    1. Find its absolute value
    2. Find the angle it makes in the complex plane in radians
  2. Given the complex number w=5i3 w=5i-3
    1. Find its modulus
    2. Find its argument in radians
  3. Given that a complex number ww makes an angle θ=3π4\theta=\frac{3\pi}{4} in the complex plane and has an absolute value w=5|w|=5, write the complex number w in rectangular form.
    Topic Notes
    ?
    There are times when we are interested in obtaining a better understanding of the properties of a complex number, such as its argument and modulus. In this section, we will learn how to calculate the argument, also known as the angle, and the modulus, also known as the magnitude or the absolute value, of a complex number.
    Notes:

    Magnitude = modulus = absolute value
    z=a2+b2 |z|= \sqrt{a^2+b^2}

    Argument = angle
    arg(z)=θ arg(z)=\theta