%E2%8B%85(%E2%88%925%2B4i).jpeg "(4−2i)⋅(−5+4i)")
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.