Adding_subtracting_complex_numbers
Learn how to add or subtract complex numbers. For example, write (2+3i)-(1+2i) as (1+i).
Challenging_complex_number_problems
This tutorial goes through a fancy problem from the IIT JEE exam in India (competitive exam for getting into their top engineering schools). Whether or not you live in India, this is a good example to test whether you are a complex number rock star.
Complex_conjugates_dividing_complex_numbers
Learn how to divide complex numbers using the conjugate of the divisor. For example, divide (2+3i) by (-1+4i) by multiplying both the dividend and the divisor by (-1-4i).
Learn how to multiply complex numbers using the fact that i^2=-1 and the distributive property. For example, multiply (1+i) by (2+3i).
Distance_midpoint_of_complex_numbers
Learn how we define the distance of two complex numbers, and how we define their midpoint.
What_are_the_imaginary_numbers_
Learn about the imaginary unit i (which is the square root of -1) and about imaginary numbers like 3i (which is the square root of -9).
Learn about complex numbers (spoiler: they are numbers that consist of both real and imaginary parts).
Multiplying_dividing_complex_numbers_in_polar_form
Learn how complex multiplication and division work when the numbers are given in polar form. Amazingly enough, this is much easier then multiplication and division in rectangular form.
Absolute_value_angle_of_complex_numbers
Learn about very important graphical features of complex numbers: their absolute value and their angle.
Learn how we can visualize complex numbers in a plane. This can be seen as an expansion of the 1-dimensional real number line into a 2-dimensional plane!
Learn how to represent complex numbers in a different way. Unlike rectangular form, which emphasizes the real and imaginary parts, polar form emphasizes the absolute value ("modulus") and the angle ("argument").
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