In this section we will perform operations with complex numbers such as addition,subtraction, multiplication and division of complex numbers. Addition/subtraction of complex numbers : The two or more complex numbers are to be added or subtracted like algebraic expression. That means like terms are to be added or subtracted. The terms with ‘i’ are like terms
Let the two complex numbers z1 = a1 + ib1 and z2= a2 + ib2
So, z1 + z2 = a1 + ib1 + a2 + ib2
= (a1 + a2) + (b1 + b2)i
Similarly for subtraction
z1 - z2 = (a1 - a2) + (b1 - b2)i Example 1 : Add (3 + 7i) and (4 + 5i) Solution : (3 + 7i) + (4 + 5i)
= 3 + 4 + 7i + 5i
= 7 + 12 i
Example 2 : Find the difference of z1 = -3 + 2i and z2 = 13 – i Solution : z2 - z1 = 13 – i –(-3 + 2i)
= 13 – i + 3 – 2i
= 16 – 3i Multiplication of complex numbers
The multiplication of complex numbers is same as the product of two binomial. Here you can use a FOIL method.
We at ask-math believe that educational material should be free for everyone. Please use the content of this website for in-depth understanding of the concepts. Additionally, we have created and posted videos on our youtube.
We also offer One to One / Group Tutoring sessions / Homework help for Mathematics from Grade 4th to 12th for algebra, geometry, trigonometry, pre-calculus, and calculus for US, UK, Europe, South east Asia and UAE students.
Affiliations with Schools & Educational institutions are also welcome.
Please reach out to us on [email protected] / Whatsapp +919998367796 / Skype id: anitagovilkar.abhijit
We will be happy to post videos as per your requirements also. Do write to us.
Russia-Ukraine crisis update - 3rd Mar 2022
The UN General assembly voted at an emergency session to demand an immediate halt to Moscow's attack on Ukraine and withdrawal of Russian troops.