Question

How do you write the complex number `z = −8` in trigonometric form?

Answer 1

`8(cos(pi/2)+isin(pi/2))`

Explanation:

`z=-8+0i`

In general `a+bi rArr r(cos(theta)+isin(theta))`
with `r=sqrt(a^2+b^2)`
and `theta ={(arctan(b/a) if a > 0),(pi/2 if a=0 and b > 0),(pi+arctan(b/a) if a < 0),(-pi/2 if a=0 and b < 0),("undefined" if a=0 and b=0):}`