Question

Нати аргумент и модуль комплексного числа Z=-^3+i. Z1=1-3i. Z2= 4+3i

Answer 1

Ты дебил220002123456789

Answer 2

To find the argument and modulus of a complex number, you can use the following formulas:

1. Argument (θ): The argument of a complex number Z = x + yi is the angle θ that the vector representing Z makes with the positive real axis in the complex plane. It can be calculated using the arctan function as follows: θ = atan2(y, x)

2. Modulus (|Z|): The modulus (also known as the absolute value or magnitude) of a complex number Z = x + yi is the distance of the point representing Z from the origin (0, 0) in the complex plane. It can be calculated as: |Z| = sqrt(x^2 + y^2)

Now, let's calculate the argument and modulus for the given complex numbers:

1. For Z = -√3 + i: x = -√3, y = 1 Argument (θ) = atan2(1, -√3) Modulus (|Z|) = sqrt((-√3)^2 + 1^2)

2. For Z1 = 1 - 3i: x = 1, y = -3 Argument (θ) = atan2(-3, 1) Modulus (|Z|) = sqrt(1^2 + (-3)^2)

3. For Z2 = 4 + 3i: x = 4, y = 3 Argument (θ) = atan2(3, 4) Modulus (|Z|) = sqrt(4^2 + 3^2)

Now, let's calculate the values:

1. For Z = -√3 + i: θ ≈ atan2(1, -√3) ≈ 1.048 radians ≈ 60 degrees (approx) |Z| ≈ sqrt((-√3)^2 + 1^2) ≈ sqrt(4) = 2

2. For Z1 = 1 - 3i: θ ≈ atan2(-3, 1) ≈ -1.249 radians ≈ -71.57 degrees (approx) |Z| ≈ sqrt(1^2 + (-3)^2) ≈ sqrt(10)

3. For Z2 = 4 + 3i: θ ≈ atan2(3, 4) ≈ 0.643 radians ≈ 36.87 degrees (approx) |Z| ≈ sqrt(4^2 + 3^2) ≈ 5

So, the arguments and moduli of the given complex numbers are approximately:

Z: Argument ≈ 60 degrees, Modulus ≈ 2 Z1: Argument ≈ -71.57 degrees, Modulus ≈ √10 (approximately 3.162) Z2: Argument ≈ 36.87 degrees, Modulus ≈ 5