Simplify and write in a+bi form: (3-4i)^2

Question

^{Simplify and write in a + bi form: (3-4i)^2}

Answer 1

(3-4i)^2 = (3-4i) * (3-4i) = 3 * 3 - 3 * 4i - 4i * 3 + 4i * 4i = 9 - 12i - 12i + 16*i*i = 9 - 24i - 16 = -7 - 24i

When faced with such a problem, try to write out explicitly the product, then multiply term by term.

Answer 2

(3 - 4i)² _{= 9 - 24i + 16i}² _{= 9 - 24i - 16 = - 7 - 24i (i}² _{= - 1 by definition)}