05 सम्मिश्र संख्याएँ और द्विघात समीकरण
अभ्यास 02
Question:
Convert each of the complex numbers given in the Exercise 3 to 8 in the polar form: 8. i
Answer:
Given: 8. i
Step 1: Convert 8. i to its algebraic form.
Answer: 8. i = 0 + 8i
Step 2: Find the magnitude of 8i.
Answer: Magnitude of 8i = 8
Step 3: Find the argument of 8i.
Answer: Argument of 8i = π/2
Step 4: Convert 0 + 8i to polar form.
Answer: 0 + 8i = 8∠(π/2)
Question:
Convert each of the complex numbers given in the Exercise 3 to 8 in the polar form: 7. √3+i
Answer:
Answer: 7. √3+i = 2 cis (π/3)
Step 1: Find the modulus (r) of the complex number = 7. √3+i
Step 2: Calculate the argument (θ) of the complex number = 7. √3+i
Step 3: Convert the complex number 7. √3+i to polar form = r cis θ
Step 4: Substitute the value of r and θ in the polar form to get the answer = 2 cis (π/3)
Question:
Find the modulus and the argument of the complex number z=−√3+i
Answer:
Answer: Modulus = 2 Argument = 3π/4
Question:
If z=1+i√3, then ∣arg(z)∣+∣arg(zˉ)∣= A π/3 B 2π/3 C 0 D π/2
Answer:
Answer: B 2π/3
Question:
Convert each of the complex numbers given in the Exercise 3 to 8 in the polar form 3 to 8 in the polar form: 3. 1−i
Answer:
Answer: 3. 1−i = r(cosθ + i sinθ)
r = √2
cosθ = 1/√2
sinθ = -1/√2
Therefore, 1−i = √2 (1/√2 + i(-1/√2)) = √2 (cos(π/4) + i sin(π/4))
Question:
Convert the given complex number in polar form : −3
Answer:
Answer: Step 1: Find the modulus (magnitude) of the given complex number, which is equal to 3.
Step 2: Find the argument (angle) of the given complex number, which is equal to 180°.
Step 3: The polar form of the given complex number is 3∠180°.
Question:
Convert each of the complex numbers given in the Exercise 3 to 8 in the polar form: 4. −1+i
Answer:
Answer: 4. r = √2, θ = -π/4
जेईई अध्ययन सामग्री (गणित)
01 सेट
02 संबंध एवं फलन
03 त्रिकोणमितीय फलन
04 गणितीय आगमन का सिद्धांत
05 सम्मिश्र संख्याएँ और द्विघात समीकरण
06 रैखिक असमानताएँ
07 क्रमचय और संचय
08 द्विपद प्रमेय
09 अनुक्रम और श्रृंखला
10 सीधी रेखाओं का अभ्यास
10 सीधी रेखाएँ विविध
11 शांकव खंड
12 त्रिविमीय ज्यामिति का परिचय
13 सीमाएं और डेरिवेटिव
14 गणितीय तर्क
15 सांख्यिकी
16 प्रायिकता