1-6i x 1+6i=37
explaian why
To solve this problem, we can use the FOIL method to multiply the given complex numbers:
(1 - 6i)(1 + 6i) = 1(1) + 1(6i) - 6i(1) - 6i(6i)
= 1 + 6i - 6i - 36i^2
Remember that i^2 is equal to -1, so we can substitute it:
(1 - 6i)(1 + 6i) = 1 + 6i - 6i - 36(-1)
= 1 + 6i - 6i + 36
= 37
Therefore, the product of (1 - 6i) and (1 + 6i) is indeed equal to 37.
To calculate the product of two complex numbers, we can use the FOIL method (First, Outer, Inner, Last) or the distributive property. Let's break down the calculation step by step:
Given expression: (1-6i) x (1+6i)
Step 1: Expand using the distributive property.
(1-6i) x (1+6i) = 1 x 1 + 1 x 6i - 6i x 1 - 6i x 6i
Step 2: Simplify the products.
= 1 + 6i - 6i - 36i^2
Step 3: Simplify the terms with 'i'.
Since i^2 is equal to -1, we can substitute it in the expression.
= 1 + 6i - 6i - 36(-1)
Step 4: Simplify further.
= 1 + 6i - 6i + 36
Step 5: Combine like terms.
= 1 + 36
Step 6: Compute the final result.
= 37
Therefore, the product of (1-6i) and (1+6i) is equal to 37.