Definition: The set of all complex numbers is Ci |r.yeR) where P-1 For any cuiip

Question

Definition: The set of all complex numbers is Ci |r.yeR) where P-1 For any cuiiplex number z E C , complex conjugate of z, denoted by !, is 1=-yi Proposition 2: IfE C, then zE R and z-21. Proposition 3: For any two complex numbers z =b, and w-r+4' for some a, b, c. d € R, we have z0E 4, Find + an" (B)-1+i (C) 1 (D) 0 5. I: 3+4i. what is the valto of sf (A) 3-4i (B) 3 +4i (C) 5 (D) 25 Consider the partial proof for Proposition 2 below: Proof (Line1) Suppose z = r + yi for some r, y € R (Line2):-= (r + yi)(z-yj: (Line) we have r'e R since 1 E R. (Line4) Similarly, we have g' R since y e R (Line5) So we have +y R since r2yeR (Line6) Therefore, zt R 6. Which of the following correctly completes (Line2) in the proof? (A) 2r 2 (B) '+2ryi-' (E) -y

Explanation / Answer

a)
i^(2014) + i^(1600)
= i^2 + 1
=-1+1
= 0

D) is correct

5) z = 3 + 4i
z *zbar = |z|^2
= (3^2 + 4^2)
= 25
D) is correct

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