-2.jpeg "(−1+8i) 2")
Simplifying (-1 + 8i)²
This article explores the process of simplifying the expression (-1 + 8i)². We'll utilize the concept of complex number multiplication and the distributive property.
Understanding Complex Numbers
Complex numbers are expressed in the form a + bi, where 'a' and 'b' are real numbers and 'i' is the imaginary unit (√-1).
Expanding the Expression
To simplify (-1 + 8i)², we expand the expression using the distributive property (FOIL method):
(-1 + 8i)² = (-1 + 8i) * (-1 + 8i)
= (-1) * (-1) + (-1) * (8i) + (8i) * (-1) + (8i) * (8i)
= 1 - 8i - 8i + 64i²
Simplifying with i² = -1
Since i² = -1, we can substitute to further simplify:
= 1 - 8i - 8i + 64(-1)
= 1 - 16i - 64
Final Result
Therefore, the simplified form of (-1 + 8i)² is -63 - 16i.