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Question
Answer the following:
Find the modulus and argument of a complex number and express it in the polar form.
− 3i
Solution
Let z = – 3i = 0 – 3i
This is of the form a + bi, where a = 0, b = – 3
∴ modulus = r
= `sqrt("a"^2 + "b"^2)`
= `sqrt(0^2 + (-3)^2)`
= `sqrt(0 + 9)`
= 3
If θ is the amplitude, then
∴ amp (z) = θ = `(3pi)/2`
∴ θ = 270° = `(3pi)/2`
∴ the polar form of z = r(cos θ + i sin θ)
= 3(cos 270° + i sin 270°)
= `3(cos (3pi)/2 + "i" sin (3pi)/2)`
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