What is the product of i2

Question

(3 − i)(6 − 7i) in standard form?
A) 25 − 27i
B) −25 − 27i
C) 11 + 27i
D) −11 + 27i

Answer 1

To find the product of \( i^2 (3 - i)(6 - 7i) \), we can follow these steps:

1. Calculate \( i^2 \): \[ i^2 = -1 \]

2. Calculate the product \( (3 - i)(6 - 7i) \) using the distributive property (also known as the FOIL method): \[ (3 - i)(6 - 7i) = 3 \cdot 6 + 3 \cdot (-7i) - i \cdot 6 - i \cdot (-7i) \] Simplifying each term: \[ = 18 - 21i - 6i + 7i^2 \] Since \( i^2 = -1 \): \[ 7i^2 = 7(-1) = -7 \] Therefore: \[ = 18 - 21i - 6i - 7 \] Combining like terms: \[ = 18 - 7 - 27i = 11 - 27i \]

3. Now include the \( i^2 \) we found earlier: \[ i^2 (11 - 27i) = -1(11 - 27i) = -11 + 27i \]

4. Final result: The product of \( i^2 (3 - i)(6 - 7i) \) is: \[ -11 + 27i \]

Thus, the answer is D) \(-11 + 27i\).