(1-3i) /(1+2i) find the modulus and amplitude in this complex number no spams
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Answers
Answer:
The modulus and argument of 1+3i/1-2i is √2 and -45° respectively.
Explanation:
Step 1: The polar form of the complex number is √2 e^{-i π/4}
The polar form of a complex number is another way to represent a complex number.
The form z=a+bi is called the rectangular coordinate form of a complex number.
Step 2:We usually measure θ so that it lies between -180 degrees to +180 degrees.
Angles measured anticlockwise from the positive x axis are conventionally positive, whereas angles measured clockwise are negative.
According to the question,
1+3i/1-2i
= 1+3i/1-2i × 1+2i/1+2i
= (1+3i)(1+2i) / (1-2i)(1+2i)
= -5+5i / 1^2 - (2i)^2
= -5+5i / 5
= -1+i
modulus =∴ r Ф = tan^-1 (b/a)
= tan^-1 (1/-1)
= tan^-1 (-1)
∴ Ф = -45°
Step 3: Polar form is given by,
z = r (cos Ф + i sin Ф)
= √2 [cos (-45° ) + i sin (-45 ° )]
= √2 [cos (45° ) - i sin (45 ° )]
∴ z= √2 e^{-i π/4}
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