How to Simplify Complex Numbers
Add the real portions together., Add the imaginary portions together., Combine the two parts to form the simplified answer.
Step-by-Step Guide
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Step 1: Add the real portions together.
Recognize that addition and subtraction are really the same process.
Subtraction is nothing more than adding a negative number.
Therefore, addition and subtraction are treated as versions of the same process.
To add two or more complex numbers, first just add the real portions of the numbers together.For example, to simplify the sum of (a+bi) and (c+di), first identify that a and c are the real number portions, and add them together.
Symbolically, this will be (a+c).
Using actual numbers instead of variables, consider the example of (3+3i) + (5-2i).
The real portion of the first number is 3, and the real portion of the second complex number is
5.
Add these together to get 3+5=8.
The real portion of the simplified complex number will be
8. -
Step 2: Add the imaginary portions together.
In a separate operation, identify the imaginary portions of each complex number and add them together.For the algebraic example of (a+bi) plus (c+di), the imaginary portions are b and d.
Adding these together algebraically gives the result (b+d)i.
Using the numerical example of (3+3i) + (5-2i), the imaginary portions of the two complex numbers are 3i and
-2i.
Adding these gives the result of 1i, which can also be written just as i. , To find the final simplified version of the sum, put the real part and the imaginary part back together.
The result is the simplified sum of the complex numbers.The sum of (a+bi) and (c+di) is written as (a+c) + (b+d)i.
Applying the numerical example, the sum of (3+3i) + (5-2i) is 8+i. -
Step 3: Combine the two parts to form the simplified answer.
Detailed Guide
Recognize that addition and subtraction are really the same process.
Subtraction is nothing more than adding a negative number.
Therefore, addition and subtraction are treated as versions of the same process.
To add two or more complex numbers, first just add the real portions of the numbers together.For example, to simplify the sum of (a+bi) and (c+di), first identify that a and c are the real number portions, and add them together.
Symbolically, this will be (a+c).
Using actual numbers instead of variables, consider the example of (3+3i) + (5-2i).
The real portion of the first number is 3, and the real portion of the second complex number is
5.
Add these together to get 3+5=8.
The real portion of the simplified complex number will be
8.
In a separate operation, identify the imaginary portions of each complex number and add them together.For the algebraic example of (a+bi) plus (c+di), the imaginary portions are b and d.
Adding these together algebraically gives the result (b+d)i.
Using the numerical example of (3+3i) + (5-2i), the imaginary portions of the two complex numbers are 3i and
-2i.
Adding these gives the result of 1i, which can also be written just as i. , To find the final simplified version of the sum, put the real part and the imaginary part back together.
The result is the simplified sum of the complex numbers.The sum of (a+bi) and (c+di) is written as (a+c) + (b+d)i.
Applying the numerical example, the sum of (3+3i) + (5-2i) is 8+i.
About the Author
John Edwards
Specializes in breaking down complex pet care topics into simple steps.
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