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Kool Kid on the block
Kool Kid on the block asked in Science & MathematicsMathematics · 3 years ago

PLE HELP WITH MY TRIG HW: Find all complex solutions *Best Answer Awarded*?

PLEASE Help. Best answer awarded

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2 Answers

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  • Pinkgreen
    Lv 7
    3 years ago
    Favorite Answer

    x^3=i

    =>

    x^3=-(i^3)

    =>

    x^3+i^3=0

    =>

    (x+i)[x^2-ix+(i^2)]=0

    =>

    (x+i)(x^2-ix-1)=0

    x+i=0

    =>x=-i

    x^2-ix-1=0

    =>

    x=[i+/-sqr(-1+4)]/2

    =>

    x=sqr(3)/2+i/2

    or

    x=-sqr(3)/2+i/2

    Ans. 3 non-real solutions:

    x=-i

    x=sqr(3)/2+i/2

    x=-sqr(3)/2+i/2

  • Φ² = Φ+1
    Lv 7
    3 years ago

    x³ = i

    Now i³ = -i, so (-i)³ = i, and so x = -i is one solution.

    This and the other two solutions are equally spaced about the unit circle centred at 0+0i

    so the other two solutions are x = -½√3 + ½ i and x = ½√3 + ½ i

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