Final Answer:
The result of the complex power operation (1 - 2i)⁶ is 117 - 44i. Option B is answer.
Step-by-step explanation:
To calculate the power of a complex number (1 - 2i)⁶, we can use the following formula:
(a + bi)⁶ = a⁶ + 6a⁵bi - 15a⁴b² - 20a³b³ + 15a²b⁴ - 6ab⁵ + bi⁶
where a and b are the real and imaginary parts of the complex number, respectively.
In this case, a = 1 and b = -2. Substituting these values into the formula, we get:
(1 - 2i)⁶ = 1⁶ + 6(1⁵)(-2i) - 15(1⁴)(-2)² - 20(1³)(-2)³ + 15(1²)(-2)⁴ - 6(1)(-2)⁵ + (-2)⁶
Simplifying the expression, we get:
1 - 12i + 60 - 160i + 120 + 96i - 64
Combining like terms, we get:
117 - 44i
Therefore, the result of the complex power operation (1 - 2i)⁶ is 117 - 44i. Option B is answer.