05 Complex Numbers and Quadratic Equations
Exercise 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
JEE NCERT Solutions (Mathematics)
01 Sets
02 Relations and Functions
03 Trigonometric Functions
04 Principle of Mathematical Induction
05 Complex Numbers and Quadratic Equations
06 Linear Inequalities
07 Permutations and Combinations
08 Binomial Theorem
09 Sequences and Series
10 Straight Lines Exercise
10 Straight Lines Miscellaneous
11 Conic Sections
12 Introduction to Three Dimensional Geometry
13 Limits and Derivatives
14 Mathematical Reasoning
15 Statistics
16 Probability