Question

Express the complex number in trigonometric form:
1-i

Answer 1

let
\[1-\iota =r \left( \cos \theta +\iota \sin \theta \right)\]
\[r \cos \theta=1,r \sin \theta=-1 \]
square and add
\[r^2=1+1=2\]
\[r=\sqrt{2}\]
\[\cos \theta=\frac{ 1 }{ \sqrt{2} },\sin \theta=\frac{ -1 }{ \sqrt{2} }\]
so\[\ theta\] lies in 4th quadrant.

Answer 2

\[\cos \theta=\cos \left( 2n \pi+2\pi-\frac{ \pi }{ 4 } \right),\theta=?\]
where n is an integer.

Answer 3

Thank you so much! I appreciate all the work it must have taken to type that out :-)

Answer 4

Is it alright if I ask a question? I'm lost on one of the steps.

Answer 5

I'm confused about how you went from the
\[rcos \Theta =1\]\[rsin \Theta= -1\]

to the part where you square and do

\[r^{2}=1+1=2\]
\[r=\sqrt{2}\]