Radian Measure

Question

Find the argument of the complex number z=I in radian measure.

 

a. pi/3

b.3pi/2

c.pi

d. pi/2

 

Please show step by step work to solution and provide final answer. Please and Thank You!

Answer 1

For the complex number z = a + bi,

if z  = 1, then a = 1, b = 0

The argument theta= arctan(b/a)= 0/1 =0,

Then theta = 0 + 2n(pi), where n= 0, 1, 2,...

but, there is no choice for answers.

If z = -1, then theta = pi, choice would be C. If z = i, then a = 0, b = 1, where z located on the Imaginary axis, which is 90 degree. Therefore, Argument theta is pi/2.

Answer 2

Is it z = i?

 

z = 0 + 1i = x + yi

 

    r = √(x²+y²) = 1

 

    x = rcosθ = cosθ = 0

 

    y = rsinθ = sinθ = 1   So, θ = π/2