Convert to Trigonometric Form |-1-2i|

Problem

−1−2*i

Solution

1. Identify the real part a and the imaginary part b from the complex number z=a+b*i

a=−1

b=−2

2. Calculate the modulus r using the formula r=√(,a2+b2)

r=√(,(−1)2+(−2)2)

r=√(,1+4)

r=√(,5)

3. Determine the argument θ using the formula tan(θ)=b/a

tan(θ)=(−2)/(−1)

tan(θ)=2

4. Adjust the angle based on the quadrant. Since both a and b are negative, the complex number lies in Quadrant III.

θ=π+arctan(2)

θ≈4.249* radians

5. Write the complex number in trigonometric form z=r*(cos(θ)+i*sin(θ))

z=√(,5)*(cos(π+arctan(2))+i*sin(π+arctan(2)))

Final Answer

−1−2*i=√(,5)*(cos(π+arctan(2))+i*sin(π+arctan(2)))

Want more problems? Check here!