Question

How do you add `(8-8i)+(-7-i)` in trigonometric form?

Answer 1

`1-9i = sqrt(82)(cos(arctan(-9)) + i sin ((arctan (-9)))`

Explanation:

Add them in rectangular form `(a + bi)` and then convert to trigonometric form:

1. Combine the like terms: `(8 + -7) + (-8i + -i) = 1-9i`
2. `r = sqrt (1^2 + (-9)^2) = sqrt (82)`
3. `theta = arctan(b/a) = arctan (-9/1) = arctan(-9)`
4. `z = r(cos theta + i sin theta)`
   `= sqrt(82)(cos(arctan(-9)) + i sin ((arctan (-9)))`