Question

समिश्र संख्या z=-√3+i का मापांक और कोणांक ज्ञात कीजिये​

Answer 1

Step-by-step explanation:

Here,

z = -sqrt(3) + i

<br> Comparing it with polar form, we get,<br>

rcostheta = -sqrt3 and rsintheta = 1

<br> Squaring and adding these two terms, we get,<br>

r^2cos^2theta+r^2sin^2theta = 4

<br>

r^2(cos^2theta+sin^2theta) = 4

<br>

r^2 = 4=> r = 2

<br> So, modulus is

2

.<br> Now,

rsintheta = 1=>sintheta = 1/2

<br>

theta = pi/6

<br> As

costheta

is negative and

sintheta

is positive, theta lies in 2nd quadrant.<br> So,

theta = pi-pi/6 = (5pi)/6

<br>