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Question
Find the modulus and amplitude of the following complex numbers.
`sqrt(3) + sqrt(2)"i"`
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Solution
Let z = `sqrt(3) + sqrt(2)"i"`
∴ a = `sqrt(3)`, b = `sqrt(2)`, i.e. a > 0, b > 0
∴ |z| = `sqrt("a"^2 + "b"^2)`
= `sqrt((sqrt(3))^2 + (sqrt(2))^2`
= `sqrt(3 + 2)`
= `sqrt(5)`
Here, `(sqrt(3), sqrt(2))` lies in 1st quadrant.
∴ amp (z) = `tan^-1("b"/"a")`
= `tan^-1(sqrt(2)/sqrt(3))`
= `tan^-1(sqrt(2/3))`
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