(8-11i).jpeg "(8-11i)(8-11i)")
Multiplying Complex Numbers: (8-11i)(8-11i)
This article explores the multiplication of the complex number (8-11i) by itself.
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 complex numbers, we use the distributive property (or FOIL method) just like with binomials.
Step 1: Expand the product using the distributive property:
(8 - 11i)(8 - 11i) = 8(8 - 11i) - 11i(8 - 11i)
Step 2: Simplify by multiplying:
= 64 - 88i - 88i + 121i²
Step 3: Substitute i² with -1:
= 64 - 88i - 88i + 121(-1)
Step 4: Combine real and imaginary terms:
= (64 - 121) + (-88 - 88)i
Step 5: Simplify:
= -57 - 176i
Conclusion
Therefore, the product of (8-11i) and itself, (8-11i)(8-11i), is -57 - 176i. This demonstrates the process of multiplying complex numbers and the resulting complex number in standard form.