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Multiplying Complex Numbers: (6i)(5i)
This article will guide you through multiplying the complex numbers (6i) and (5i).
Understanding Complex Numbers
Complex numbers are numbers that consist of a real part and an imaginary part. The imaginary part is denoted by the letter 'i', where i² = -1.
Multiplication of Complex Numbers
To multiply complex numbers, we follow the distributive property, just like we would with regular algebraic expressions.
Let's multiply (6i) and (5i):
(6i)(5i) = (6 * 5) * (i * i)
= 30 * i²
Since i² = -1, we can substitute:
= 30 * (-1)
= -30
Therefore, (6i)(5i) = -30.
Key Points:
- Remember that i² = -1.
- When multiplying complex numbers, treat 'i' as a variable.
- Apply the distributive property to simplify the multiplication.
This example shows how multiplying complex numbers can lead to a real number as a result. Understanding the properties of complex numbers and their multiplication is crucial for solving problems in various mathematical fields.