%5E2.jpeg "(6+7i)^2")
Squaring Complex Numbers: (6 + 7i)^2
This article will guide you through the process of squaring the complex number (6 + 7i).
Understanding Complex Numbers
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 the square root of -1 (i.e., i² = -1).
Squaring (6 + 7i)
To square (6 + 7i), we essentially multiply it by itself:
(6 + 7i)² = (6 + 7i) * (6 + 7i)
We can expand this using the distributive property (or FOIL method):
(6 + 7i) * (6 + 7i) = 6 * 6 + 6 * 7i + 7i * 6 + 7i * 7i
Simplifying:
= 36 + 42i + 42i + 49i²
Since i² = -1:
= 36 + 42i + 42i - 49
Combining real and imaginary terms:
= -13 + 84i
Conclusion
Therefore, the square of the complex number (6 + 7i) is -13 + 84i.