(3i)(-2i)(5i)

2 min read Jun 16, 2024
(3i)(-2i)(5i)

Simplifying Complex Number Multiplication: (3i)(-2i)(5i)

This article will guide you through the process of simplifying the multiplication of complex numbers: (3i)(-2i)(5i).

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.

Simplifying the Expression

Let's break down the multiplication step-by-step:

  1. Multiply the first two factors: (3i)(-2i) = -6i²

  2. Substitute i² with -1: -6i² = -6(-1) = 6

  3. Multiply the result by the third factor: 6(5i) = 30i

Therefore, the simplified form of (3i)(-2i)(5i) is 30i.

Key Points to Remember

  • i² = -1 is a fundamental property of complex numbers.
  • The product of two complex numbers is another complex number.
  • Remember to treat 'i' as a variable when multiplying.

By understanding these concepts, you can easily simplify any multiplication involving complex numbers.

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