How do you write the complex number in trigonometric form #-9-2sqrt10i#?

Question

1840 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-10-06T10:54:51

In trigonometric form expressed as #11(cos3.754+isin3.754)#

#Z=a+ib #. Modulus: #|Z|=sqrt (a^2+b^2)#;

Argument:#theta=tan^-1(b/a)# Trigonometrical form : #Z =|Z|(costheta+isintheta)#

#Z=-9-2sqrt10 i #. Modulus:

#|Z|=sqrt((-9)^2+(-2sqrt10)^2) =sqrt(81+40)=sqrt121=11#

Argument: #tan alpha= ((|2sqrt10|))/(|9|)= 0.7027 #. #alpha =tan^-1(0.7027) = 0.61255#

Z lies on third quadrant, so #theta =pi+alpha=pi+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]