Question

given that =-1/2+i√3/2 find the modulus and argument of z​

Answer 1

Step-by-step explanation:

let

a+ib= -1/2+i root3/2

thus,

a=-1/2 and b= root3/2

modulus |a+ib| = squareroot(a^2+b^2)

=

$\sqrt{ {( - 1 \div 2)}^{2} + {( \sqrt{3 } \div 2)}^{2} }$

$\sqrt{1 \div 4 + 3 \div 4}$

sqroot(4/4)=1

now real part is negative and imaginary part is positive, hence the angle falls in second quadrant.

thus arg(a+ib) = pi +arc tan (b/a)

pi + arctan (root3/2/-1/2)

= pi+arctan(-root3)

180 degree + (- 60 degree)

180-60

=120 degree