Question

find the module and argument of the complex number -1-i√3
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Answer 1

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Answer:

z = -1 - i√3 = a + ib

here, a = -1 and b = -√3

|z| = √a^2 + b^2

so, √(-1)^2 + (-√3)^2

= √1+3

= √4

= 2

the modulus of the complex number - 1 - i√3 is 2

its in third quadrant so,

tanø = b/a

= √3/1

tanø = √3

tan60° = √3

ø = 60° = π/3

ø = π/3 - π

ø = -2π/3

the argument of the complex number is -2π/3

so, 2( cos -2π/3 + sin -2π/3 )

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