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=-9-2sqrt10 i Z=−9−2√10i. Modulus:
|Z|=sqrt((-9)^2+(-2sqrt10)^2) =sqrt(81+40)=sqrt121=11|Z|=√(−9)2+(−2√10)2=√81+40=√121=11
Argument: tan alpha= ((|2sqrt10|))/(|9|)= 0.7027 tanα=(∣∣2√10∣∣)|9|=0.7027. alpha =tan^-1(0.7027) = 0.61255α=tan−1(0.7027)=0.61255
Z lies on third quadrant, so theta =pi+alpha=pi+0.61255 ~~ 3.754θ=π+α=π+0.61255≈3.754
:. Z=11(cos3.754+isin3.754) , argument theta in radians
Z= 11cos3.754+11sin3.754i
In trigonometric form expressed as 11(cos3.754+isin3.754)[Ans]
