This is a free lesson from our course in Algebra II In this lesson you'll explore how to add or subtract complex numbers.You'll find here some examples with solution, and the instructor explains all that with the help of audio, video presentation and in own hand writing. Complex numbers are added, subtracted, and multiplied by applying the associative, commutative and distributive laws, together with i = -1.To add complex numbers we make use of a technique that you  have seen before. This involves collecting together like terms. Let's start by adding two algebraic expressions. Suppose we want to add 6 + 2t and 4 + 3t. The terms 6 and 4 are simply numbers. The terms 2t and 3t both contain t and are like terms. We collect the like terms together and simplify. So 6 + 2t + 4 + 3t =    (6 + 4) + (2t + 3t) = 10 + 5t.(More text below video...)
Other useful lessons:
 Imaginary Unit Plotting complex numbers on a 2D plane Multiply and Divide the complex numbers Classification of roots using the discriminant Solving quadratic equation with imaginary roots
(Continued from above) Adding complex numbers works in exactly the same way. All you have to do is to add together the real parts and add together the imaginary parts of the two complex numbers to get the answer. Subtraction works in a very similar way. You have to subtract together the real parts and subtract together the imaginary parts of the two complex numbers to get the answer.If z1 = a1 + ib1 and z2 = a2 + ib2 be two complex number, then
z1 + z2 = (a1 + a2) + i(b1 + b2) and z1 - z2 = (a1 - a2) + i(b1 - b2). For example, if z1 = 4 + 7i and z2 = 6 + 9i
z1 + z2=(4 + 7i) + (6 + 9i)=(4 + 6) + i(7 + 9) = 10 + 16i
z1 - z2=(4 + 7i) - (6 + 9i)=(4 - 6) + i(7 - 9) = -2 - 2i
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