Question

How to find the trigonometric form of the number -6+i ? Thank you.

Round any angles to four decimal places

Answer 1

`-6 + i = sqrt(37) (cos(2.976) + i sin(2.976)) = sqrt(37) e^(2.976 i)`

Explanation:

`"Step 1 is calculating the modulus of the number."`
`| -6 + i | = sqrt(6^2 + 1) = sqrt(37)`
`"Step 2 is multiplying and dividing through that modulus."`
`-6 + i = sqrt(37) (-6/sqrt(37) + i/sqrt(37))`
`"Step 3 is calculating the angle with arctan()."`
`theta = arctan(1/-6) = arctan(-1/6) = -9.462 °`
`"But we need to convert the angle to the second quadrant"`
`"where cos < 0 and sin > 0, so we need to add 180° :"`
`theta = -9.462 ° + 180 ° = 170.5 ° = 2.976" rad (radians)"`
`=> -6 + i = sqrt(37) (cos(2.976) + i sin(2.976)) = sqrt(37) e^(2.976 i)`