Question

How do you simplify $(2-3i)+(-2-5i)$ ?

Answer 1

In this question, we have to simplify the given term. Since it contains complex numbers, therefore, we will apply the basic mathematical rules and the distributive property to get the solution. We first open the brackets of the given problem, that is apply the distributive property $a(b-c)=ab-ac$ and then constitute the constants together and the iota terms together. Then we simplify more by canceling the same terms with opposite signs and make further calculations, to get the required result for the problem.

Complete step-by-step solution:
According to the question, we have to simplify the given complex number.
So, we will use the basic mathematical rules and the distributive property to solve the same.
The complex term given to us is $(2-3i)+(-2-5i)$ ---------- (1)
We will first apply the distributive property $a(b-c)=ab-ac$ in equation (1), here a=1, b=-2, and c=-5i, therefore we get
$2-3i+(-2)+(-5i)$
On further simplification, we get
$2-3i-2-5i$
Now, we take to constitute the constant together and the complex number together, we get
$2-2-3i-5i$
Now, we know that the same terms with opposite signs cancel out each other, therefore we get
$-3i-5i$
On further simplification, we get
$-8i$
Therefore, for the complex number $(2-3i)+(-2-5i)$ , its simplified answer is equal to $-8i$.

Note: While solving this problem, keep in mind the formula you are using. Do mention them in each step wherever is applicable to avoid confusion and mathematical errors. At the final result, that is -8i we cannot solve the a single iota, therefore, we conclude our answer there only.