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- Imaginary and Complex Numbers

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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.

8.

Imaginary and Complex Numbers

8.1

Introduction to imaginary numbers

8.2

Complex numbers and complex planes

8.3

Adding and subtracting complex numbers

8.4

Complex conjugates

8.5

Multiplying and dividing complex numbers

8.6

Distance and midpoint of complex numbers

8.7

Angle and absolute value of complex numbers

8.8

Polar form of complex numbers

8.9

Operations on complex numbers in polar form

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Get Started Now8.1

Introduction to imaginary numbers

8.2

Complex numbers and complex planes

8.3

Adding and subtracting complex numbers

8.4

Complex conjugates

8.5

Multiplying and dividing complex numbers

8.6

Distance and midpoint of complex numbers

8.7

Angle and absolute value of complex numbers

8.8

Polar form of complex numbers

8.9

Operations on complex numbers in polar form