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Question
Express the following complex numbers in polar form and exponential form:
− i
Solution
Let z = − i = 0 − i
∴ a = 0, b = − 1
∴ z lies on negative imaginary Y-axis.
∴ |z| = r
= `sqrt("a"^2 + "b"^2)`
= `sqrt(0^2 + (-1)^2`
= 1
and arg z = 270° = `(3pi)/2`
∴ the polar form of z = r(cos θ + i sin θ)
= 1 (cos 270° + i sin 270°)
= `1(cos (3pi)/2 + "i" sin (3pi)/2)`
The exponential form of z = reiθ = `"e"^((3pi)/2"i")`
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