Question

if z=-1 + i be a complex number .then arg(z) is equal ​

Answer 1

Z= -1+i

comparing the given complex number with

Z = x+iy, we get,

x=-1 & y=1

tanθ=y/x= -1

or, θ = π-π/4= 3π/4

arg z = 3π/4

Answer 2

The value of arg(z) is 3π/4.

Given:

z = -1 + i

To Find:

The value of arg(z).

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 i = $\sqrt{-1}$.

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 as,

arg(z) = θ = $tan^{-1} \frac{y}{x}$

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

∴ The value of arg(z) is 3π/4.

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