Home > Trigonometry > The Trigonometric Form of Complex Numbers

If #z=tanalpha+itanbeta#, find the modulus and argument of #z#?

Answer 1

Zoe Austin

#|z|=sqrt(tan^2alpha+tan^2beta)#

and #arg|z|=tan^(-1)(tanbeta/tanalpha)#

As for a comlex number #z_0=x+iy#, #|z|=sqrt(x^2+y^2)# and #arg|z|=tan^(-1)(y/x)#

Hence for #z=tanalpha+itanbeta#

#|z|=sqrt(tan^2alpha+tan^2beta)#

and #arg|z|=tan^(-1)(tanbeta/tanalpha)#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Elijah Alexander

The modulus of ( z ) is ( \sqrt{\tan^2(\alpha) + \tan^2(\beta)} ), and the argument of ( z ) is ( \arctan(\frac{\tan(\beta)}{\tan(\alpha)}) ).

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.