![]() Since 0 can be written as 0 + 0i, it follows that adding this to a complex number will not change the value of the complex number.Īddition on the Complex Plane – The Parallelogram Rule The sum of any complex number and zero is the original number. (z 1 + z 2) + z 3 is the same as z 1 + (z 2 + z 3) When 3 or more complex numbers are added, the sum is the same regardless of how the numbers are grouped. Addition of complex numbers is associative.The order in which the complex numbers are added does not matter. Addition of complex numbers is commutative.For example, if z 1, z 2 and z 3 are all complex numbers of the form a+bi: The other usual properties for addition also apply to complex numbers. You just gather all the imaginary terms together and add them as like terms. And no not radical as in extreme – radical as in something under a root sign □ And luckily for us, the rules for adding and subtracting complex numbers is pretty similar to something you have seen before in algebra – collecting like terms.Ĭonsider the expression (2x + 6) + (3x + 2).Ħ and 2 are just numbers which can be added together, and since 2x and 3x both contain x (same variable, same exponent), they can be added together because they are like terms. The same is true of complex numbers – since they are also just numbers, they can be added and subtracted, provided you apply the rules. Again, this was made possible by learning some additional rules. ![]() And for each of these, you learnt about the rules you needed to follow – like finding the lowest common denominator when adding fractions.įrom there you went on to learn about adding and subtracting expressions with variables. You then learnt how to add and subtract fractions. Well, you probably started off by learning how to add and subtract natural numbers. So how did you learn to add and subtract real numbers? You should be familiar with adding and subtracting ordinary numbers (I really hope so! And to be honest, if not, this article aint for you! :))
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