Question

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CLASS 11 MATH


If Z =−1 + і be a complex number .Then Arg(Z) is equal to 


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Answer 1

Step-by-step explanation:

Given,

z=1+i

z=1+i

modulus: ∣z∣=

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

=

$\sqrt{2}$

=2

θ=tan¹(1/1) =tan¹(1)

argument: ∴θ= π/4

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Answer 2

Solution:

A complex number is any number of the form

z = x+iy

where

x = the real part and

y = the imaginary part.

Here 'i' is the imaginary number and

$\:  \sqrt{-1}−1$

Argument of a complex number 'z' (denoted by θ) is the value of the angle subtended by the x-axis and the line joining 'z' and the origin. It is calculated a

$arg(z) = θ = tan^{-1} \frac{y}{x}tan−1xy</p><p>$

We are given a complex number z = -1 + i.

Here,

The real part, x = -1

The imaginary part, y = 1.

Note that since x is negative and y is positive, z lies in the second quadrant.

Hence,

$arg(z) = π - tan^{-1} (\frac{1}{-1})tan−1(−11) =π -  tan^{-1}( -1)tan−1(−1) = π - π/4 = 3π/4.$