• 2021 April(Z04) Math Question 55

    Number Types & Properties

    - Complex Number

    Complex Number
    Choice B

    Given that

    ι={−1}\iota = \sqrt\{-1\}
    {ι+ι4+ι3}{ι3+ι4+ι5}=?\frac\{\iota + \iota^4+\iota^3\}\{\iota^3 + \iota^4+\iota^5\}=?

    As we know that

    ι2=−1,  ι4=1,  ι3=−ι\iota^2=-1,\; \iota^4=1,\; \iota^3=-\iota

    So,

    ∴{ι+ι4+ι3}{ι3+ι4+ι5}={ι−1−ι}{−ι+1+ι}=−{1}{1}\therefore \frac\{\iota + \iota^4+\iota^3\}\{\iota^3 + \iota^4+\iota^5\}=\frac\{\iota -1-\iota\}\{-\iota + 1+\iota\}=-\frac\{1\}\{1\}
    =−1=-1

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