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- Imaginary and Complex Numbers

Still Confused?

Try reviewing these fundamentals first.

Still Confused?

Try reviewing these fundamentals first.

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- Lesson: 1b2:20
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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.

Basic concepts: Distance formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$, Solving expressions using 45-45-90 special right triangles ,

Related concepts: Imaginary zeros of polynomials, Magnitude of a vector, Direction angle of a vector,

Notes:

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

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

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

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

- 1.Given the complex number $z=2+3i$

a)Find its absolute valueb)Find the angle it makes in the complex plane in radians - 2.Given the complex number $w=5i-3$

a)Find its modulusb)Find its argument in radians - 3.Given that a complex number $w$ makes an angle $\theta=\frac{3\pi}{4}$ in the complex plane and has an absolute value $|w|=5$, write the complex number w in rectangular form.

47.

Imaginary and Complex Numbers

47.1

Introduction to imaginary numbers

47.2

Complex numbers and complex planes

47.3

Adding and subtracting complex numbers

47.4

Complex conjugates

47.5

Multiplying and dividing complex numbers

47.6

Distance and midpoint of complex numbers

47.7

Angle and absolute value of complex numbers

47.8

Polar form of complex numbers

47.9

Operations on complex numbers in polar form

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Get Started Now47.1

Introduction to imaginary numbers

47.2

Complex numbers and complex planes

47.3

Adding and subtracting complex numbers

47.4

Complex conjugates

47.5

Multiplying and dividing complex numbers

47.6

Distance and midpoint of complex numbers

47.7

Angle and absolute value of complex numbers

47.8

Polar form of complex numbers

47.9

Operations on complex numbers in polar form