Perform the indicated operations and write the answer in the form a + bi, where a and b are real numbers.

Problem #1 (3+2i)squared

Problem #2 icubed-isquared

#1 Multip[ly out (3 + 2i)^2 and use the fact that i^2 = -1.

#2 i^2 = -1, and i^3 = -i
Add the two terms for the answer

I need this in a final answer form please :)

Then go somewhere else. We are here to help you learn, not do your work for you.

Wow drwls....that was pretty rude and entirely unnecessary!!

Actually Dawn, I agree with him. You are looking for answers, not help. See my post on the other.

http://www.jiskha.com/display.cgi?id=1265727367

i did the work on them...they werent right...i just want to know if im right after i try to solve the problem...thanks

Show us your steps in the future and we'll gladly tell you where you went wrong, if the problem happens again.

I did in the math post I did right after this one....perhaps u can see if I still did it wrong? Thanks.....

To perform the indicated operations and write the answers in the form a + bi, we first need to know a few rules for working with complex numbers. For problem #1 and problem #2, we'll use the following rules:

Rule #1: To square a complex number (a + bi)², we can use the formula:

(a + bi)² = a² + 2abi + (bi)²

Rule #2: To find the cube of a complex number (a + bi)³, we can use the formula:

(a + bi)³ = a³ + 3a²bi + 3ab²(i²) + (bi)³

Rule #3: Remember that i² is equal to -1. So, whenever we see i² in an expression, we can replace it with -1.

Now let's apply these rules to solve problem #1 and problem #2:

Problem #1: (3 + 2i)²
Using the formula from Rule #1, we get:
(3 + 2i)² = 3² + 2(3)(2i) + (2i)²
Simplifying further:
(3 + 2i)² = 9 + 12i + 4(i²)
Since i² is equal to -1, we replace it:
(3 + 2i)² = 9 + 12i + 4(-1)
(3 + 2i)² = 9 + 12i - 4
(3 + 2i)² = 5 + 12i

Therefore, the answer is 5 + 12i.

Problem #2: i³ - i²
Using the formula from Rule #2 and Rule #1, we get:
i³ - i² = (0 + 1i)³ - (0 + 1i)²
Simplifying further:
i³ - i² = 0³ + 3(0)²(1i) + 3(0)(1i)² + (1i)³ - (0 + 1i)²
Since i² is equal to -1 and i³ is equal to -i, we replace them:
i³ - i² = 0 + 3(0)(1i) + 3(0)(-1) + (-i) - (-1)
Simplifying further:
i³ - i² = 0 + 0 - 0 - i +1
i³ - i² = 1 - i

Therefore, the answer is 1 - i.