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    can someone help me with this question:

    1)z=-3+4i
    given that z=(a+i)^4 where a is real find the values for a such that

    z is real
    z is wholly imaginary

    2)
    then, given that a+bi is the conjugate of (a+bi)^2 find all possible pairs of values for a and b.

    not sure how to answer either question any help appreciated.
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    (Original post by trebor00)
    can someone help me with this question:

    1)z=-3+4i
    given that z=(a+i)^4 where a is real find the values for a such that

    z is real
    z is wholly imaginary

    2)
    then, given that a+bi is the conjugate of (a+bi)^2 find all possible pairs of values for a and b.

    not sure how to answer either question any help appreciated.
    1: Begin with the binomial expansion of (a+i)^4 and then rearrange it into the form x+yi. From here, what do you need to make it real or wholly imaginary?

    2: Expand (a+bi)^2 and find its conjugate in the form x+yi, which is equal to a+bi. Then we may say a=x and b=y since we are equating real and imaginary parts.
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    (Original post by trebor00)
    can someone help me with this question:

    1)z=-3+4i
    given that z=(a+i)^4 where a is real find the values for a such that

    z is real
    z is wholly imaginary

    2)
    then, given that a+bi is the conjugate of (a+bi)^2 find all possible pairs of values for a and b.

    not sure how to answer either question any help appreciated.
    Are you sure you posted the first question correctly?

    z = -3+4i ?
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    (Original post by trebor00)
    can someone help me with this question:

    1)z=-3+4i
    given that z=(a+i)^4 where a is real find the values for a such that

    z is real
    z is wholly imaginary

    2)
    then, given that a+bi is the conjugate of (a+bi)^2 find all possible pairs of values for a and b.

    not sure how to answer either question any help appreciated.
    For 1) I'm unsure what's the purpose of your defined z at the start, but just expand your (a+i)^4 then make the real bit =0 for purely imaginary z, and then make the imaginary part =0 for purely real z.

    For 2) Just expand it, and make it equal the conjugate of a+bi. Solve as required for pairs of values.
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    can someone show me how to do the first part of the first question as I still don't get it.
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    (Original post by trebor00)
    can someone show me how to do the first part of the first question as I still don't get it.
    Do you get how to expand (a+i)^4?
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    yes binomial expansion
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    (Original post by trebor00)
    yes binomial expansion
    OK, so I don't see how you're unable to do the question.

    After expanding, you want to get your answer in the form of z=(a+\mathbf{i})^4=f(a)+\mathbf{  i}g(a)

    For z to be real, you want to set g(a)=0 and find the values of a which satisfy this.

    For z to be purely imaginary, you want to set f(a)=0 instead.
 
 
 
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