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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...

    are these the correct answers??

    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 -

    is this the answer bob purley??? thanks for your help!!

  • 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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