find the modulus and argument of 1+√3i​

Question

find the modulus and argument of
1+√3i​

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Mary 4 weeks 2021-08-18T13:55:00+00:00 1 Answer 0 views 0

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    2021-08-18T13:56:50+00:00

    Answer:

    Modulus is 4

    Argument is 60°

    Step-by-step explanation:

    Given complex number is 1+√3i

    Modulus of complex number x + iy is

     \sqrt{ {x}^{2} +  {y}^{2}  }

    Modulus of given complex number is

     \sqrt{ {1}^{2}  +  { \sqrt{3} }^{2} }

     \sqrt{1 + 3}

     \sqrt{4}

    2

    Now argument of a complex number is

    tan^{ - 1} \frac{y}{x}

    tan^{ - 1} \frac{ \sqrt{3} }{1}

    tan^{ - 1} \sqrt{3}

     \frac{\pi}{3}

    => 60°

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