Z=a+ib Z=a+ib. Modulus: |Z|=sqrt (a^2+b^2)|Z|=√a2+b2; Argument:theta=tan^-1(b/a)θ=tan−1(ba) Trigonometrical form : Z =|Z|(costheta+isintheta)Z=|Z|(cosθ+isinθ)
Z=5/2(sqrt3-i)= 5/2sqrt3 -5/2i Z=52(√3−i)=52√3−52i. Modulus |Z|=sqrt(( 5/2sqrt3 )^2+(-5/2)^2) =sqrt(75/4+25/4)=sqrt25=5|Z|=√(52√3)2+(−52)2=√754+254=√25=5
Argument: tan theta= (-cancel(5/2))/(cancel(5/2)sqrt3)= -1/sqrt3 . Z lies on fourth quadrant, so theta =tan^-1(-1/sqrt3) = -pi/6=-30^0 or theta = 360-30=330^0 :. Z=5(cos330+isin330)
In trigonometric form expressed as 5(cos330+isin330)[Ans]
