Multiplying Complex Numbers: (6+5i)(32i)
This article will guide you through the process of multiplying two complex numbers: (6+5i) and (32i).
Understanding Complex Numbers
Complex numbers are numbers that can be expressed in the form a + bi, where:
 a and b are real numbers
 i is the imaginary unit, defined as the square root of 1 (i² = 1)
Multiplying Complex Numbers
To multiply two complex numbers, we use the distributive property, just like we would with any binomial multiplication.

Expand the product:
(6+5i)(32i) = 6(3) + 6(2i) + 5i(3) + 5i(2i)

Simplify:
= 18  12i + 15i  10i²

Substitute i² = 1:
= 18  12i + 15i + 10

Combine real and imaginary terms:
= (18 + 10) + (12 + 15)i

Final result:
= 28 + 3i
Conclusion
Therefore, the product of (6+5i) and (32i) is 28 + 3i.
This process can be applied to multiply any pair of complex numbers, remembering to use the distributive property and substitute i² with 1.