Convert to Trigonometric Form 7i

Problem

7*i

Solution

1. Identify the complex number in standard form z=a+b*i where a=0 and b=7

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

r=√(,0+7)

r=√(,49)

r=7

3. Determine the argument θ by identifying the position of the point (0,7) on the complex plane.

4. Observe that the point lies on the positive imaginary axis, which corresponds to an angle of 90 or π/2 radians.

θ=π/2

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

z=7*(cos(π/2)+i*sin(π/2))

Final Answer

7*i=7*(cos(π/2)+i*sin(π/2))

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