Convert to Trigonometric Form square root of 3-i

Problem

√(,3)−i

Solution

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

a=√(,3)

b=−1

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

r=√(,(√(,3))2+(−1)2)

r=√(,3+1)

r=2

3. Determine the argument θ by finding the angle in the fourth quadrant (since a>0 and b<0 such that tan(θ)=b/a

tan(θ)=(−1)/√(,3)

θ=(11*π)/6

4. Substitute the values of r and θ into the trigonometric form z=r*(cos(θ)+i*sin(θ))

z=2*(cos((11*π)/6)+i*sin((11*π)/6))

Final Answer

√(,3)−i=2*(cos((11*π)/6)+i*sin((11*π)/6))

Want more problems? Check here!