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Principal value of amplitude of (1+i) is:

  • Option 1)

    \frac{\pi}{4}

  • Option 2)

    \frac{\pi}{2}

  • Option 3)

    \frac{3\pi}{4}

  • Option 4)

    \pi

 

Answers (1)

best_answer

As learnt in concept

Definition of Argument/Amplitude of z in Complex Numbers -

\theta =tan^{-1}|\frac{y}{x}|, z\neq 0

\boldsymbol{\theta,\pi-\theta,-\pi+\theta,-\theta} are Principal Argument if z lies in first, second, third or fourth quadrant respectively.

- wherein

 

 In (1+i), tan\theta=1, thus \theta=\frac{\pi}{4}


Option 1)

\frac{\pi}{4}

This is correct option

Option 2)

\frac{\pi}{2}

This incorrect option

Option 3)

\frac{3\pi}{4}

This incorrect option

Option 4)

\pi

This incorrect option

Posted by

Plabita

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