Question

Simplify (3-2i)².
(a) 5−12i
(b) 13+12i
(c) −5+12i
(d) −13−12i

Answer 1

To simplify (3-2i)², expand the square using the formula (a-b)² = a² - 2ab + b². Simplify further by substituting i² = -1. The correct answer is option C.

Step-by-step explanation:

To simplify (3-2i)², we need to expand the square. Using the formula (a-b)² = a² - 2ab + b², we can apply it to the complex number (3-2i) as follows:

(3-2i)² = (3)² - 2(3)(-2i) + (-2i)²

Expanding further gives:

(9 + 12i + 4i²)

Since i² = -1, we can simplify the expression to:

9 + 12i - 4

Which simplifies to:

5 + 12i