Title MP DPP Sheet 12.pdf ✅

1 North Delhi : 56-58, First Floor, Mall Road, G.T.B. Nagar (Near Metro Gate No. 3), Delhi-09, Ph: 011-41420035 South Delhi : 28-A/11, Jia Sarai, Near-IIT Metro Station, New Delhi-16, Ph : 011-26851008, 26861009 IIT JAM PHYSICS 2025 (Online Batch) SECTION: MATHEMATICAL PHYSICS Daily Practice Problem (DPP) Sheet 12: Complex Analysis (Basic Preview of Complex Numbers - II) ; PART - A: MULTIPLE CHOICE QUESTIONS (MCQ) Q.1. If 2 1, ,   are the complex cube roots of unity, then     5 5 2 2 1 1          will be (a) 4 (b) 8 (c) 16 (d) 32 Q.2. If 2 1, ,   are the complex cube roots of unity, then the value of the following expression:   2 1      2 4 1      4 8 1      8 16 1    .... to 2n factors (a) 2n (b) 22n (c) 0 (d) 1 Q.3. If 2 1, ,   are the complex cube roots of unity, then the value of the expression 2 2 2 1 1 1 1 1 1 1 1 2 2 .......... n n                                           (a)   1 2 2 3 n n  (b)   1 2 2 3 n n  (c)   1 2 1 3 n n  (d)   1 2 1 3 n n  Q.4. If z is a complex number such that 2 z z   1 0 , then the sum of the folloing series 2 2 2 2 2 3 6 2 3 6 1 1 1 1 z z z z .......... z z z z                                 (a) 6 (b) 12 (c) 18 (d) 24 Q.5. The expression 1 sinh x  can be simplified to (a)   2 ln 1 x x   (b)   2 ln 1 x x   (c)   2 ln 1 x x   (d)   2 ln 1 x x   Q.6. The expression 1 tan z  can be written as (a) 1 ln 2 1 i iz iz         (b) ln 2 i i z i z         (c) ln 2 i i z i z         (d) 1 ln 2 1 i iz iz          Q.7. The principal value of lni is equal to (a) 0 (b) i / 2 (c) i / 2 (d) i