Solution: [√(5+12i)+ √(5-12i)]/[√(5+12i)- √(5-12i)] Multiply numerator and denominator with √(5+12i)+√(5-12i) [√(5+12i)+√(5-12i)√(5+12i)+√(5-12i)]/[√(5+12i)-√(5-12i)√(5+12i)+√(5-12i)] = (5+12i+2(5+12i)(5-12i)+(5-12i)/(5+12i)-(5-12i) = (10+2√(25+144))/24i = 10+2(13)/24i = 36/24i =... View Article
Solution: Since inequality in complex numbers is not defined, a+ib> c+id is possible if b = 0 and d =... View Article
Solution: (1+i)2/(2-i) = (1+2i-1)/(2-i) = 2i/(2-i) = 2i(2+i)/(2-i)(2+i) = (4i-2)/(4+1) = (4i-2)/5 Imaginary part is 4/5. Hence option (3) is... View Article
Solution: Let z = x+iy z’ = x-iy zz’ = (x+iy)(x-iy) = x2+ixy-ixy+y2 = x2+y2 Given z.z’ = z x2+y2... View Article
Solution: (1-i)2/(3-i) = (1-2i-1)/(3-i) = -2i/(3-i) Multiply numerator and denominator with (3+i) = -2i(3+i)/(3-i)(3+i) = (-6i+2)/(9+1) = (2-6i)/10 = (1-3i)/5... View Article
Solution: [1/(1-2i)]+[3/(1+i)](3+4i)/(2-4i) = (1+i+3(1-2i))(3+4i)/(1-2i)(1+i)(2-4i) = (4-5i)(3+4i)/(3-i)(2-4i) = (12-15i+16i+20)/(6-2i-12i-4) = (32+i)/(2-14i) = (32+i)(2+14i)/(2-14i)(2+14i) = (64+2i+448i-14)/(4+196) = (50+450i)/200 = (1+9i)/4 Hence option... View Article
Solution: Additive inverse of x+iy is -(x+iy). Additive inverse of 1-i is -(1-i) = -1+i Hence option (3) is the... View Article
(1) Re (z1) Re (z2) (2) Re (z1) Im (z2) (3) Im (z1) Re (z2) (4) None of these Solution:... View Article
Solution: a = cos θ+ i sin θ (1+a)/(1-a) = (1+cos θ+ i sin θ)(1-cos θ+i sin θ)/(1-cos θ-i sin... View Article
Solution: Given 3-2yi = 9x-7i Comparing real and imaginary parts 9x = 3 x = ½ = 0.5 2y =... View Article
Solution: i+i2+i3+….1000 terms = i-1-i+1 …1000 terms = 0
Solution: eiθ = cos θ+ i sin θ eiπ/2 = cos π/2+ i sin π/2 = i Let (a+ib) =... View Article
Solution: (1+2i)/(1-2i) Multiply numerator and denominator with (1+2i) =(1+2i)(1+2i)/(1-2i)(1+2i) = (1+4i-4)/(1+4) = (-3+4i)/5 = -(⅗)+(⅘)i It lies in second quadrant.... View Article
Solution: (1+i)8+(1-i)8 (1+i)2 = (1+2i-1) = 2i ((1+i)2)4 = (2i)4 = 16 (1-i)2 = (1-2i-1) = -2i ((1-i)2)4 = (-2i)4... View Article
Solution: In+in+1+in+2+in+3 = in(1+i+i2+i3) = in(1+i-1-i) = 0 Hence option (1) is the answer.
Solution: x+1/x = 2 cos θ Rearranging , we get x2+1-2x cos θ = 0 x2-2x cos θ +1 =... View Article
Solution: i(1+3+5..(2n+1) 1+3+5+…(2n+1) = sum of (n+1) terms of A.P Sn+1 =[ (n+1)/2](2+n+1-1)2 = [(n+1)/2](2+2n) = (n+1)2 Put n =... View Article
A bacteria will have the following cell organelles: Plasma membrane Cytoplasm Nucleoid (DNA or RNA) Ribosomes Most bacteria also have... View Article
A typical eukaryotic cell would have the following components: Nucleus Cell wall Cell membrane Ribosome Mitochondria Chloroplast Golgi bodies Main... View Article
The organelles inside a prokaryotic cell includes: Nucleoid (DNA or RNA) Ribosomes Plasma membrane Cytoplasm Read More Only at BYJU’S... View Article
