Final answer:
To multiply (9i)(9i), we compute (9 x 9) and (i x i), which gives us 81 and i^2. Since i^2 equals -1, the final result is 81 multiplied by -1, which simplifies to -81.
Step-by-step explanation:
The question asks us to multiply and simplify the expression (9i)(9i). To approach this, we recognize 'i' as the imaginary unit, which is defined by the property that i2 = -1. When multiplying two complex numbers in the form of a real number times an imaginary number, we use the distributive property.
Multiplying the given expression, we have 9i times 9i or (9 x 9) and (i x i). Carrying out the multiplication, 9 times 9 equals 81, and i2 equals -1, so our final simplified result is 81 times -1, which equals -81.
Therefore, the result of multiplying (9i)(9i) simplifies to -81.