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Question
Answer the following:
Find the modulus and argument of a complex number and express it in the polar form.
8 + 15i
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Solution
Let z = 8 + 15i
∴ a = 8, b = 15, a, b > 0
∴ |z| = r
`sqrt("a"^2 + "b"^2)`
= `sqrt((8)^2 + (15)^2`
= `sqrt(64 + 225)`
= `sqrt(289)`
= 17
Here, (8, 15) lies in 1st quadrant
∴ amp (z) = θ = `tan^-1("b"/"a") = tan^-1(15/8)`
∴ the polar form of z = r(cos θ + i sin θ)
= 17(cosθ + i sinθ), where θ = `tan^-1(15/8)`
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