জটিল সংখ্যার যোগ ও বিয়োগ

To add complex numbers, you add the real parts and their imaginary parts separately. The sum of the two complex numbers $a+bi$ and $c+di$ becomes $(a+c)+(b+d)i$.

Similarly, you subtract the real parts and imaginary parts separately to subtract complex numbers. The difference of the two complex numbers $a+bi$ and $c+di$ becomes $(a-c)+(b-d)i$.

Let's try some Complex Number Arithmetic.

First take a look at this very quite simple example.

Now try it with complex numbers.

You got the hang of it? Let's now try the sum of complex numbers.

Moving on to multiplication!

Finally, exponents.

That's it for complex arithmetic! Not so complex, huh?

To add two complex numbers $a+bi$ and $c+di,$ simply add their corresponding parts to get $(a+c)+(b+d)i.$ To subtract, simply subtract their corresponding parts to get $(a-c)+(b-d)i.$

(Video) Graphing, Adding, and Subtracting Complex Numbers

by PatrickJMT

Here's a good video by PatrickJMT going over the basics of complex numbers. Inequalities and equalities will be solved the same way as real numbers, but now we just have imaginary terms.

Also remember: $$i=\sqrt{-1}\\ i^2=-1\\ i^3=-i\\ i^4=1$$ They cycle after this. So $i^5$ will just equal $i$ and $i^6=-1$ and so on.

$$4(3+i) + 2(8-i)\\ 12 + 4i + 16 - 2i\\ 28 + 2i$$

Done!

(Videos) Complex Number Arithmetic

by mathman1024

Here's a video by mathman1024 explaining how to add and subtract complex numbers. The standard form for complex numbers is $a+bi$. An quick example is $3+5i$.

So adding or subtracting complex numbers is super easy. You add or subtract the real parts and add or subtract the imaginary parts. In other words, you combine like terms. The first example he looks at is: $(5+7i)+(3-12i)$. $$\begin{align} &(5+7i)+(3-12i)\\ =&5+7i+3-12i\\ =&8-5i \end{align}$$

He goes over another example. Try this yourself and see if you get the same answer.

1. $(11-3i)-(2+10i)$

He then does an example about multiplying a complex number. He does a simple example: $5(3-7i)$. To solve this we just apply the distributive property. $$\begin{align} &5(3-7i)\\ =&5*3-5*7i\\ =&15-35i \end{align}$$

He goes over another example. Try this yourself and see if you get the same answer.

1. $4i(7+8i)$

In this video he combines adding and subtracting with multiplying.

The first example is: $5(7-4i)-3i(10+5i)$. $$\begin{align} &5(7-4i)-3i(10+5i)\\ =&35-20i-30i-15i^2\\ =&35-20i-30i-15(-1)\\ =&50-50i \end{align}$$