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Question
Find the modulus and amplitude of the following complex numbers.
1 + i
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Solution
Let z = 1 + i
∴ a = 1, b = 1, i.e. a > 0, b > 0
∴ |z| = `sqrt("a"^2 + "b"^2)`
= `sqrt(1^2 + 1^2)`
= `sqrt(1 + 1)`
= `sqrt(2)`
Here, (1, 1) lies in 1st quadrant
amp (z) = `tan^-1("b"/"a")`
= tan–1(1)
= `pi/4`
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