Final answer:
The square of the complex number (6-5i) is calculated using the binomial squaring formula and substituting i2 with -1, resulting in 61 - 60i.
Step-by-step explanation:
To square the complex number (6-5i), we follow the algebraic rule for squaring binomials which is (a-b)2 = a2 - 2ab + b2. Applying this to our complex number, we get:(6-5i)2 = 62 - 2(6)(5i) + (5i)2= 36 - 60i - 25i2Since i2 = -1, we can replace -25i2 with 25 to get:= 36 - 60i + 25= 61 - 60i
This represents the squared complex number in standard form.To square a complex number, you need to multiply it by itself. To square (6-5i), multiply it by itself:(6-5i)^2 = (6-5i)(6-5i)Using the distributive property, you can expand this expression:(6-5i)(6-5i) = 6(6) - 6(5i) - 5i(6) + 5i(5i)Simplify the expression:36 - 30i - 30i + 25i^2Since i^2 = -1, substitute that in:36 - 30i - 30i + 25(-1)Simplify further:36 - 60i + 25(-1)Finally, combine like terms:36 - 60i - 25The final answer is -11 - 60i.To square the complex number (6-5i), we follow the algebraic rule for squaring binomials which is (a-b)2 = a2 - 2ab + b2. Applying this to our complex number, we get:(6-5i)2 = 62 - 2(6)(5i) + (5i)2= 36 - 60i - 25i2Since i2 = -1, we can replace -25i2 with 25 to get:= 36 - 60i + 25= 61 - 60i