Still Confused?

Try reviewing these fundamentals first.

- Home
- ACT Compass Test Prep
- Imaginary and Complex Numbers

Still Confused?

Try reviewing these fundamentals first.

Still Confused?

Try reviewing these fundamentals first.

Nope, I got it.

That's that last lesson.

Start now and get better math marks!

Get Started NowStart now and get better math marks!

Get Started NowStart now and get better math marks!

Get Started NowStart now and get better math marks!

Get Started Now- Lesson: 1a16:31
- Lesson: 1b7:04
- Lesson: 1c7:49
- Lesson: 2a9:46
- Lesson: 2b6:20
- Lesson: 2c8:37
- Lesson: 311:22

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

38.

Imaginary and Complex Numbers

38.1

Introduction to imaginary numbers

38.2

Complex numbers and complex planes

38.3

Adding and subtracting complex numbers

38.4

Complex conjugates

38.5

Multiplying and dividing complex numbers

38.6

Distance and midpoint of complex numbers

38.7

Angle and absolute value of complex numbers

38.8

Polar form of complex numbers

38.9

Operations on complex numbers in polar form

We have over 2080 practice questions in ACT Compass Test Prep for you to master.

Get Started Now38.1

Introduction to imaginary numbers

38.2

Complex numbers and complex planes

38.3

Adding and subtracting complex numbers

38.4

Complex conjugates

38.5

Multiplying and dividing complex numbers

38.6

Distance and midpoint of complex numbers

38.7

Angle and absolute value of complex numbers

38.8

Polar form of complex numbers

38.9

Operations on complex numbers in polar form