Solution: For adding complex numbers z and w, we will use the formula (a + ib) + (c + id) = (a + c) + i(b + d). The final answer is then converted into polar form.Įxamples of Adding and Subtracting Complex NumbersĮxample 1: Add the two complex numbers z = 3 – 6i and w = -5 + 4i.

For addition and subtraction of complex numbers in polar form, the complex numbers must first be converted to rectangle form.

Subtracting complex numbers violates the law of commutativity.

All real numbers are complex, but not all complex numbers are always real.Thus, we only need to mix similar phrases. Complex number addition and subtraction is identical to the addition and subtraction of two binomials.Hence, it holds the closure property.Ĭommutative Property: The addition of complex numbers is commutative but the subtraction of complex numbers is not commutative.Īssociative Property: Adding complex numbers is associative but the subtraction of complex numbers is not associative.Īdditive Identity: 0 is the additive identity of the complex numbers, i.e., for a complex number z, we have z + 0 = 0 + z = z.Īdditive Inverse: For a complex number z, the additive inverse in complex numbers is -z, i.e., z + (-z) = 0 Important Notes on Adding and Subtracting Complex Numbers Listed below are the addition and subtraction properties of complex numbers:Ĭlosure Property: The sum and difference of complex numbers is also a complex number. Properties of Adding and Subtracting Complex Numbers Step 4: Give the final answer in a + ib format. Step 3: Add (subtract) the imaginary parts of the complex numbers. Step 2: Add (subtract) the real parts of the complex numbers. Step 1: Segregate the real and imaginary parts of the complex numbers. The steps for adding and subtracting complex numbers are as follows:

Next, we shall analyse the procedure for the same in detail. Now we know the addition and subtraction formulas for complex numbers. Steps and Rules for Adding and Subtracting Complex Numbers

Adding and subtracting complex numbers