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Question

How do you find the principal argument of z=3i ?


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Solution

Finding the principal argument:

Step 1: find the principal argument of complex number

z=x+iy which can be written as z=rcosθ+irsinθ

where x=rcosθ and y=rsinθ

Step 2: Substituting the values

z=3i

0=rcosθ and 3=rsinθ

By squaring and adding the above values we get,

r2(cos2θ+sin2θ)=9

r=9=3

cosθ=0,sinθ=1θ=π2

Hence, the principal argument of z=3i is θ=π2.


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