If z is a complex number $3 + 4 i$ the modulus of $¯ z$ is

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Solution

$z = 3 + 4 i ⟹ ¯ z = 3 - 4 i | z | = \sqrt{x^{2} + y^{2}} | ¯ z | = \sqrt{3^{2} + 4^{2}} | ¯ z | = \sqrt{25} = 5$

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z = \frac{1 - i}{3 - 4 i}

If z is a complex number of unit modulus, the value of $\frac{2 + 2 z}{3 + 3 ¯ z}$ is

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θ

arg (\frac{1 + z}{1 + ¯ z}) =

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a r g (\frac{1 + z}{1 + ¯ z})

(\frac{3 + 4 i}{1 - 2 i})

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