Expanding (73i)^2
This article will guide you through the steps of expanding the expression (73i)^2.
Understanding Complex Numbers
Before we start, let's understand what complex numbers are. A complex number is a number that can be expressed in the form a + bi, where 'a' and 'b' are real numbers and 'i' is the imaginary unit, defined as i^2 = 1.
Expanding the Expression
To expand (73i)^2, we can use the formula (a  b)^2 = a^2  2ab + b^2. Here's how it works:

Identify 'a' and 'b': In this case, a = 7 and b = 3i.

Substitute the values: (73i)^2 = 7^2  2(7)(3i) + (3i)^2

Simplify:
 7^2 = 49
 2(7)(3i) = 42i
 (3i)^2 = 9i^2 = 9(1) = 9

Combine the terms: 49  42i  9

Final answer: (73i)^2 = 40  42i
Conclusion
By using the formula for expanding a binomial squared, we have successfully expanded (73i)^2 to get 40  42i. This process demonstrates how complex numbers can be manipulated and simplified through algebraic operations.