compute the modulus and argument of each complex number. Plot and label each complex number in the complex plane given.
(a) 1 + i
(b) square root3 + i
(c) -2i
(d)-5
(e)5-5i
(f) 7 square root3+7i
(g) −3 + 4i
Answers
Given : a) 1 + i
(b) square root3 + i
(c) -2i
(d)-5
(e)5-5i
(f) 7 square root3+7i
(g) −3 + 4i
To Find : compute the modulus and argument of each complex number.
Plot and label each complex number in the complex plane
Solution:
Z = x +iy
मापांक = | Z | = √x² + y²
कोणांक = tan⁻¹ ( y/x) = arg(z)
Magnitude (modulus) = = | Z | = √x² + y²
Angle or argument = tan⁻¹ ( y/x) = arg(z)
1 + i
| Z | = √1² + 1² = √2
arg(z) = tan⁻¹(1/1) = π/4
√3 + i
| Z | = √√3² + 1² = 2
arg(z) = tan⁻¹(1/√3) = π/6
-2i
| Z | = 2
arg(z) = 3π/2 or - π/2
-5
| Z | = 5
arg(z) = π
5-5i
| Z | = 5√2
arg(z) = -π/4 or 7π/4
and so on
Learn More:
Geometrically, the modulus of a complex number represents its ...
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Every real number is a complex number. Proof - Brainly.in
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