How do you find a trigonometric form of a complex

Ella Bradshaw

Ella Bradshaw

Answered question

2022-01-30

How do you find a trigonometric form of a complex number?

Answer & Explanation

Emilie Booker

Emilie Booker

Beginner2022-01-31Added 14 answers

Let z=x+iy a complex number in algebraic form.
z=r(cosϕ+isinϕ) is its trigonometric form, where:
r=x2+y2 is the modulus of the number and
if x>0
ϕ=arctan(yx)
if x<0
ϕ=arctan(yx)
if x<0
ϕ=arctan(yx)+π
if x=0and y>0
ϕ=π2.
if x=0and y<0
ϕ=32π
if x=y=0

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