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Question
Find the modulus and amplitude of the following complex numbers.
`1 + "i"sqrt(3)`
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Solution
Let z = `1 + "i"sqrt(3)`
∴ a = 1, b = `sqrt(3)`, i.e. a > 0, b > 0
∴ |z| = `sqrt("a"^2 + "b"^2)`
= `sqrt(1^2 + (sqrt(3))^2)`
= `sqrt(1 + 3)`
= 2
Here, (1, `sqrt(3)`) lies in 1st quadrant
amp (z) = `tan^-1("b"/"a")`
= `tan^-1(sqrt(3))`
= `pi/3`
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