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Convert the complex number (-16)/(1+isqr...

Convert the complex number `(-16)/(1+isqrt(3))`into polar form.

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To convert the complex number \(\frac{-16}{1 + i\sqrt{3}}\) into polar form, we will follow these steps: ### Step 1: Multiply by the Conjugate To eliminate the imaginary part in the denominator, we multiply the numerator and denominator by the conjugate of the denominator, which is \(1 - i\sqrt{3}\). \[ z = \frac{-16}{1 + i\sqrt{3}} \cdot \frac{1 - i\sqrt{3}}{1 - i\sqrt{3}} = \frac{-16(1 - i\sqrt{3})}{(1 + i\sqrt{3})(1 - i\sqrt{3})} \] ...
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Knowledge Check

  • Convert the complex number (1+isqrt(3)) into polar form.

    A
    `2(cos""(pi)/(3)+isin ""(pi)/(3))`
    B
    `(cos""(pi)/(3)+isin ""(pi)/(3))`
    C
    `2(cos""(pi)/(6)+isin ""(pi)/(6))`
    D
    None of these
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