Q82.If the real part of the complex number z = 1−3i3+2i coscos θθ , θ ∈(0, π2 ) is zero, then the value of sin2 3θ + cos2 θ is equal to ______.
What This Question Tests
This question involves performing division of complex numbers, setting the real part to zero to find the value of an angle, and then evaluating a trigonometric expression.
Concepts Tested
Formulas Used
(a+ib)/(c+id) = (ac+bd)/(c^2+d^2) + i(bc-ad)/(c^2+d^2)
cos^2(x) = (1+cos(2x))/2
sin^2(x) = (1-cos(2x))/2
📚 NCERT Sections This Tests
8.2 — Name The Following Compounds According To Iupac System Of Nomenclature:
Chemistry Class 12 · Chapter 8
8.2 Name the following compounds according to IUPAC system of nomenclature: (i) CH3CH(CH3)CH2CH2CHO (ii) CH3CH2COCH(C2H5)CH2CH2Cl (iii) CH3CH=CHCHO (iv) CH3COCH2COCH3 (v) CH3CH(CH3)CH2C(CH3)2COCH3 (vi) (CH3)3CCH2COOH (vii) OHCC6H4CHO-p
8.17 — Complete Each Synthesis By Giving Missing Starting Material, Reagent Or Products
Chemistry Class 12 · Chapter 8
8.17 Complete each synthesis by giving missing starting material, reagent or products
2.1 — Two Charges 5 × 10–8 C And –3 × 10–8 C Are Located 16 Cm Apart. At
Physics Class 11 · Chapter 2
2.1 Two charges 5 × 10–8 C and –3 × 10–8 C are located 16 cm apart. At what point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.
📋 Question Details
- Chapter
- Complex Numbers
- Topic
- Properties of complex numbers
- Year
- 2021
- Shift
- 27 Jul Shift 2
- Q Number
- Q82
- Type
- Numerical
- NCERT Ref
- Class 11 Mathematics Ch 5: Complex Numbers and Quadratic Equations
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