Multiplying Complex Numbers: (62i)(23i) in Standard Form
This article will guide you through the process of multiplying the complex numbers (62i) and (23i) and expressing the result in standard form (a + bi).
Understanding Complex Numbers
Complex numbers are expressed in the form a + bi, where:
 a is the real part
 b is the imaginary part
 i is the imaginary unit, defined as the square root of 1 (i² = 1)
Multiplication of Complex Numbers
When multiplying complex numbers, we treat them like binomials and use the distributive property (or FOIL method):
(6  2i)(2  3i) = (6 * 2) + (6 * 3i) + (2i * 2) + (2i * 3i)
Simplifying the Expression

Multiply the terms: 12  18i  4i + 6i²

Substitute i² with 1: 12  18i  4i + 6(1)

Combine real and imaginary terms: (12  6) + (18  4)i

Simplify: 6  22i
Final Result
Therefore, the product of (62i) and (23i) in standard form is 6  22i.