Question

Please help me how to multiply

Answer 1

You got 81-36i because you simply squared each term individual. However, in order to square the term, you must multiply the terms like this: (9-6i)(9-6i)

To multiply these terms, you use a process called FOILing. The letters stand for first, outer, inner, last, referring to the parts of the equation that you multiply. After you multiply all four times, you add the terms. You do so as following;

First: the first terms in both parts. 9 x 9 = 81
Outer: the first term in the first section, and the second term in the second. 9 x -6i = -54i
Inner: the second term in the first section, and the first term in the second. -6i x 9 = -54i
Last: the second term in both parts. -6i x -6i = 36i^2. In math, i = the square root of -1, so i^2 is -1. multiply 36 by -1 and you get -36.

After all the multiplication, you get: 81-54i-54i-36. After combining like terms, you finish with 45-108i.

Answer 2

$Use:(a-b)^2=a^2-2ab+b^2\\-------------------------------\\\\(9-6i)^2=9^2-2\cdot9\cdot6i+(6i)^2=81-108i+36i^2\\\\=81-108i+36(-1)=81-108i-36=45-108i\\\\-------------------------------\\\\i=\sqrt{-1}\to i^2=1$