(4−2i)⋅(−5+4i)

2 min read Jun 16, 2024
(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.

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