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- Imaginary and Complex Numbers

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Knowing the argument and the modulus of a complex number allows us to convert a complex number from its rectangular form, which is what we have been using thus far, to its other basic form – polar form. We will see that while a complex number in rectangular form is denoted by its horizontal and vertical components, a complex number in polar form is denoted by its magnitude and argument.

Basic concepts: Distance formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$, Use tangent ratio to calculate angles and side (Tan = $\frac{o}{a}$ ), Solving expressions using 45-45-90 special right triangles , Solving expressions using 30-60-90 special right triangles ,

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

- 1.Convert the following complex numbers from rectangular form to polar forma)$z=2i-3$b)$w=-5-3i$c)$z=4-i$
- 2.Convert the following complex numbers from polar form to rectangular forma)$z=4(\cos(\frac{\pi}{4})+i\sin(\frac{\pi}{4}))$b)$w=13(\cos(180^{\circ})+i\sin(180^{\circ}))$c)$z=4(\cos(\frac{5\pi}{3})+i\sin(\frac{5\pi}{3}))$
- 3.Given that $z=4-3i$, and $w=2-i$, find $z+w$ and express it in polar 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