Question

If z =1 - cos theta + i sin theta, then |z| =

a)2sin theta/2
b)2cos theta/2
c)2|sin theta/2|
d)2|costheta/2|

point to be noted : 1) |z| is the modulus of z
2)answer it fast ​

Answer 1

Step-by-step explanation:

hope it will be helpful for u...

Answer 2

Given:

$z = 1 - cos\beta + isin\beta$

To find:

|Z| = modulus of Z

Solution:

Modulus of a complex number is defined as the distance of point Z from origin or we can also define modulus of a complex number as the absolute value of a complex number.

let Z be a complex number Z = x + iy , then

$|Z|= \sqrt{x^{2}+ y^{2} }$

as mentioned in the question,

$z = 1 - cos\beta + isin\beta$

$|z| = \sqrt{(1-cos\beta) ^{2}+sin ^{2}\beta }$

solve ,

$|z|= \sqrt{cos^{2}\beta +sin^{2}\beta +1 -2cos\beta }$

$cos^{2}\beta +sin^{2}\beta = 1$

$1-cos2\beta = 2sin^{2}\beta$

Modulus of Z is (c)