- #1

chwala

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- Homework Statement
- Find, in the form ##x+iy##, the complex numbers given in the polar coordinate form by;

##z=2\left[\cos \dfrac{3π}{4} + i \sin \dfrac{3π}{4}\right]##

- Relevant Equations
- complex numbers

This is the question as it appears on the pdf. copy;

##z=2\left[\cos \dfrac{3π}{4} + i \sin \dfrac{3π}{4}\right]##

My approach;

##\dfrac{3π}{4}=135^0##

##\tan 135^0=-\tan 45^0=\dfrac{-\sqrt{2}}{\sqrt{2}}##

therefore,

##z=-\sqrt{2}+\sqrt{2}i##

There may be a better approach.

##z=2\left[\cos \dfrac{3π}{4} + i \sin \dfrac{3π}{4}\right]##

My approach;

##\dfrac{3π}{4}=135^0##

##\tan 135^0=-\tan 45^0=\dfrac{-\sqrt{2}}{\sqrt{2}}##

therefore,

##z=-\sqrt{2}+\sqrt{2}i##

There may be a better approach.