Respuesta :
Answer:
The answer is the last one, D, pictured above on the question, I took the test and it showed it was the right one
Step-by-step explanation:
The geometric expression of two complex number is the magnitude r₁*r₂ and the phase is θ₁ + θ₂.
What is complex number?
The complex number is" the combination of real numbers and an imaginary number. The complex number is of the form a + i b".
According to the question,
z, w are the two complex numbers. The distance from its point in the complex plane to the origin (0,0) and the angle formed by the line segment from the origin to the point and the positive half of the x-axis.
The distance or 'magnitude' to the origin is denoted as 'r' and the angle or 'phase' formed denoted as 'θ'. The distance to the origin is called 'magnitude'.
The parameter 'r' and 'θ' related to 'a' along x-axis and 'b' along y-axis.
Euclidean distance formula applying Pythagorean theorem we have
r = [tex]\sqrt{a^2+b^2}[/tex].
The sine angle is defined to the ratio y-coordinate 'b' to length 'r' and the cosine angle is defined to the ratio x-coordinate 'a' to length 'r'.
sin θ = [tex]\frac{b}{r}[/tex] and cos θ = [tex]\frac{a}{r}[/tex].
b = r sin θ; a = r cosθ
When multiplying two complex numbers we by multiplying magnitude together and add two phase. when divide two complex number by dividing the magnitude correspondingly and subtracting the phase from the numerator and the denominator.
Then we have product complex number to the magnitude r₁ and phase θ₁
with a complex number to the magnitude r₂ and the phase θ₂ which gives the complex number with magnitude r₁ * r₂ and θ₁ + θ₂.
Hence, the geometric representation of z w is with magnitude r₁*r₂ and phase is θ₁ + θ₂.
Learn more about complex numbers here
https://brainly.com/question/14654281
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