Convert to Trigonometric Form 54i

Problem

54*i

Solution

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

a=0

b=54

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

r=√(,0+54)

r=54

3. Determine the argument θ by identifying the position on the complex plane. Since the number lies on the positive imaginary axis, the angle is 90 or π/2 radians.

θ=π/2

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

z=54*(cos(π/2)+i*sin(π/2))

Final Answer

54*i=54*(cos(π/2)+i*sin(π/2))

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