Convert to Trigonometric Form 5i

Problem

5*i

Solution

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

a=0

b=5

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

r=√(,0+5)

r=5

3. Determine the argument θ by identifying the position of the point (0,5) on the complex plane.

Since the point lies on the positive imaginary axis, *θ=π/2

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

z=5*(cos(π/2)+i*sin(π/2))

Final Answer

5*i=5*(cos(π/2)+i*sin(π/2))

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