# math

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

Problem #1 (3+2i)^2
Problem #2 i^3 - i^2

• math -

Notice the following pattern of powers of i
i = √-1
i^2 = √-1√-1 = -1
i^3 =i(i^2) = i(-1) = -i
i^4 = (i^2)(i^2) = (-1)(-1) = +1
i^5 = i(i^4) = i(1) = i
Can you see the pattern

for your first question , just expand it like you would (a+b)^2, then replace the powers of i

for the second, you should be able to do it following the above patterns

• math -

thanks...can I ask u to tell me if I'm correct when I do the problems please and repost back?

• math -

Reiny...

problem #1: (3+2i)^2=
(a+b)^2=
(3+2times-1)=
(3+1)^2=
4^2= 16

problem #2: i^3-i^2=
a-b=
-i- -1

??????????????????????????

• math -

No, not right

(3+2i)^2= 9+12i+4i^2= 9+12i-4=5+12i
check that.

• math -

• math -

You need to check it and answer for yourself it is it right.

• math -

it makes sense now...thanks!!

• math -

PROBLEM 2....

i^3 - i^2=
-i + the square root of -1^2=
-i + 1i

is this correct?

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