Question 394202: For the complex number 5+6i find the value of θ (theta) in the trigonometric form (answer to the nearest hundredth of a degree).
I have a test on complex numbers tomorrow and this kind of problem will be on it. I don't understand it at all, so thank you for any help on this.
Answer by CharlesG2(834)   (Show Source):
You can put this solution on YOUR website! "For the complex number 5+6i find the value of θ (theta) in the trigonometric form (answer to the nearest hundredth of a degree).
I have a test on complex numbers tomorrow and this kind of problem will be on it. I don't understand it at all, so thank you for any help on this."
when complex numbers are plotted in x + iy (standard cartesian form) the x axis is the Real numbers, the y-axis is the Imaginary axis, the iy gets plotted against the y-axis
in trigonometric form:
the distance r from the origin to where z = x + iy is plotted is the hypotenuse of a right triangle
the x-leg equals rcos(θ)
the y-leg equals rsin(θ)
θ (theta) is the angle between the line r makes and the real (x) axis
r = sqrt(x^2 + y^2)
z = rcos(θ) + risin(θ) = r(cos(θ) + isin(θ))
5 + 6i is in quadrant I, the quadrants are numbered clockwise
r = sqrt(5^2 + 6^2)
r = sqrt(25 + 36)
r = sqrt(61)
θ = atan(abs(y/x)), where atan is arctangent, and abs means absolute value
θ = atan(abs(y/x)) = atan(6/5)
θ = 50.19 degrees to the nearest hundredth
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