(−2−3i)⋅(−5−2i)

2 min read Jun 17, 2024

Multiplying Complex Numbers: (−2−3i)⋅(−5−2i)

This article will guide you through multiplying the complex numbers (−2−3i) and (−5−2i). We will use the distributive property and the fact that i² = -1.

Step 1: Distribute

We will distribute the first complex number, (−2−3i), to each term of the second complex number, (−5−2i):

(−2−3i)⋅(−5−2i) = (−2)⋅(−5) + (−2)⋅(−2i) + (−3i)⋅(−5) + (−3i)⋅(−2i)

Step 2: Simplify

Now we can simplify each term:

(−2)⋅(−5) = 10
(−2)⋅(−2i) = 4i
(−3i)⋅(−5) = 15i
(−3i)⋅(−2i) = 6i²

Step 3: Substitute i² = -1

Since i² = -1, we can substitute this into our expression:

10 + 4i + 15i + 6i² = 10 + 4i + 15i + 6(-1)

Step 4: Combine Like Terms

Finally, we can combine the real and imaginary terms:

10 + 4i + 15i - 6 = (10 - 6) + (4 + 15)i

The Answer

Therefore, (−2−3i)⋅(−5−2i) = 4 + 19i.