(5−5i)⋅(−3+5i)

Jasonbradley

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Jun 16, 2024

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Multiplying Complex Numbers: (5 - 5i) * (-3 + 5i)

This article will demonstrate the process of multiplying two complex numbers, (5 - 5i) and (-3 + 5i).

Understanding Complex Numbers

A complex number is a number 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.

Multiplication of Complex Numbers

To multiply complex numbers, we use the distributive property, just like we would with any binomial multiplication.

Here's how we multiply (5 - 5i) * (-3 + 5i):

1. Distribute: (5 - 5i) * (-3 + 5i) = 5(-3) + 5(5i) - 5i(-3) - 5i(5i)

2. Simplify: -15 + 25i + 15i - 25i²

3. Remember i² = -1: -15 + 25i + 15i - 25(-1)

4. Combine real and imaginary terms: (-15 + 25) + (25 + 15)i

5. Final result: 10 + 40i

Therefore, the product of (5 - 5i) and (-3 + 5i) is 10 + 40i.