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The amplitude and modulus of the complex number -2 + 23i. is

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The amplitude and modulus of the complex number $- 2 + 23 i .$ is $4$ and $\frac{π}{3}$ .

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Noah Discussed

The amplitude and modulus of the complex number

- 2 + 23 i .

4

and

\frac{π}{3}

14 mins ago

Discuss this question LIVE

14 mins ago

Text solutionVerified

The given complex number is

- 2 + 23 i

The modulus of

- 2 + 23 i = (- 2)^{2} + (23)^{2} = 4 + 12 = 16 = 4

Therefore, the modulus of

- 2 + 23 i = 4

Clearly, in the z-plane the point

z = - 2 + 23 i = (- 2, 23)

lies in the second quadrant. Hence, if

am p z = θ

then,

t an θ = (23) / - 2 = - 3

where,

π /2 < θ \leq π

Therefore,

t an θ = - 3 = t an (π - \frac{π}{3}) = t an [\frac{2 π )}{3}]

Therefore,

θ = \frac{2 π}{3}

Therefore, the required amplitude of

- 2 + 23 i

\frac{2 π}{3} .

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Question Text	The amplitude and modulus of the complex number $- 2 + 23 i .$ is $4$ and $\frac{π}{3}$ .
Answer Type	Text solution:1
Upvotes	150