Question 1 Find the modulus and the argument of the complex number z= -1 - i.3^(1/2)
Class X1 - Maths -Complex Numbers and Quadratic Equations Page 108
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You can find tge detailed way of answering this question in Ncert pg no.107 ex 7 ... However, I have done answered your question and attached it below!!
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sorry for my grammar, I actually went on writing it never checked back, anyways I guess the basic concept is clear !!
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concept :- if z = x + iy is a complex number then,
|z| = √(x² +y²) .
for argument:-
tan∅ = |y/x| and then , use the quadrant concept.
solution:-
z = -1 - √3i
|z| = √{(-1)² +(-√3)²}
= √(1 + 3) = √4 = 2
tan∅ = |y/x| = |-√3/-1| = √3 = tanπ/3
∅ = π/3
but here, imaginary part→negative
real part → negative
so, ∅ lies on 3rd quadrant.
hence, arg(z) = -π+∅
= -π + π/3 = -2π/3
|z| = √(x² +y²) .
for argument:-
tan∅ = |y/x| and then , use the quadrant concept.
solution:-
z = -1 - √3i
|z| = √{(-1)² +(-√3)²}
= √(1 + 3) = √4 = 2
tan∅ = |y/x| = |-√3/-1| = √3 = tanπ/3
∅ = π/3
but here, imaginary part→negative
real part → negative
so, ∅ lies on 3rd quadrant.
hence, arg(z) = -π+∅
= -π + π/3 = -2π/3
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