Question

Express the complex number in trigonometric form. -4

Answer 1

The standard form for a complex number is:
\[a+ib\]
or
\[x+iy\]
where:
"a" and "x" are the real parts of the complex number, and;
"b" and "y" being the imaginary part of the complex number.
when you want to find the trigonometric form you're looking for the mod-arg form:
\[Rcis\theta=R(\cos\theta + i\sin\theta)\]
Where R is the modulus of the complex number;
"cos(theta)" being the real part;
"sin(theta)" being the imaginary part, and;
"theta" being the argument of the complex number.
For your example being -4.
We should find the the modulus first using the Phythagorean formula:
\[R=\sqrt{a^2+b^2}\]
\[=\sqrt{(-4)^2+0^2}\]
\[=\sqrt{16}\]
\[=4\]
Now you should find the angle or argument of -4. Use this graph to find the angle you're looking for:

Then you can connect all the information you gathered- the modulus (the distance) and the argument (the angle); so now you can put all that into the mod-arg form given to you by me.