## Multiplying Complex Numbers: (4−2i)⋅(−5+4i)

This article will guide you through multiplying the complex numbers (4−2i) and (−5+4i).

### Understanding Complex Numbers

Complex numbers are numbers that can be expressed in the form **a + bi**, where *a* and *b* are real numbers, and *i* is the imaginary unit, defined as the square root of -1 (i.e., **i² = -1**).

### Multiplying Complex Numbers

Multiplying complex numbers is similar to multiplying binomials. We use the **distributive property** to expand the product:

(4−2i)⋅(−5+4i) = 4(−5) + 4(4i) − 2i(−5) − 2i(4i)

### Simplifying the Expression

Now, let's simplify the expression:

**-20 + 16i + 10i - 8i²**

Remember that **i² = -1**, so we can substitute:

- -20 + 16i + 10i - 8(-1)

Combining real and imaginary terms:

- (-20 + 8) + (16 + 10)i

### The Final Answer

Finally, we obtain the product:

**(4−2i)⋅(−5+4i) = -12 + 26i**

Therefore, the product of (4−2i) and (−5+4i) is the complex number **-12 + 26i**.