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...)
(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 z_{1} = a_{1} + ib_{1} and z_{2} = a_{2} + ib_{2} be two complex number, then z_{1} + z_{2} = (a_{1} + a_{2}) + i(b_{1} + b_{2}) and z_{1}  z_{2} = (a_{1}  a_{2}) + i(b_{1}  b_{2}). For example, if z_{1} = 4 + 7i
and z_{2} = 6 + 9i z_{1} + z_{2}=(4
+ 7i) + (6 + 9i)=(4 + 6) + i(7 + 9) = 10 + 16i z_{1}  z_{2}=(4
+ 7i)  (6 + 9i)=(4  6) + i(7  9) = 2  2i
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