Solution: (a+bω+cω2)/(b+cω+aω2) + (a+bω+cω2)/(c+aω+bω2) = [(a+bω+cω2)/(b+cω+aω2)]+(a+bω+cω2)ω/(c+aω+bω2)ω = [(a+bω+cω2)(1+ω)]/(b+cω+aω2) Multiply numerator and denominator with ω = [(a+bω+cω2)(1+ω)ω]/(b+cω+aω2)ω = [(a+bω+cω2)(1+ω)ω]/(a+bω+cω2) = (1+ω)ω... View Article
Solution: (cos 300+i sin 300)/(cos 600-i sin 600) = [(√3/2)+i (½) ]/[(1/2)-(√3/2)i] = (√3+i)/(1-i√3) Multiply numerator and denominator with (1+i√3)... View Article
Solution: Let z = x+iy |z| = √(x2+y2) …(i) Given |(z-25)/(z-1)| = 5 |(z-25)| = 5|(z-1)| |(x+iy-25)| = 5|(x+iy-1)| Squaring... View Article
Solution: |(z-i)/(z+i)| = 5 |(z-i)| = 5|(z+i)| Take z = x+iy |(x+(y-1)i| = 5|(x+(y+1)i| x2+(y-1)2 = 25(x2+(y+1)2) x2+y2-2y+1 = 25x2+25y2+50y+25... View Article
Solution: ω = z/(z-(⅓)i) |ω| = 1 |ω| = |z/(z-(⅓)i)| |z| = |(z-(⅓)i)| Put z = x+iy |3x+i(3y-1)| = |3(x+iy)|... View Article
Solution: Given |z1|= 12 (circle 1) |z2 – 3 – 4i| = 5 (circle 2) Min |z1-z2| = 12-10 =... View Article
Solution: Given |z + 4| ≤ 3 |z + 1| = |z + 4-3| = |z + 4|+|-3| ≤ 3+3... View Article
Solution: |(z-i)/(z+i)| = 2 |(z-i)| = 2|(z+i)| Take z = x+iy |(x+(y-1)i| = 2|(x+(y+1)i| x2+(y-1)2 = 4(x2+(y+1)2) x2+y2-2y+1 = 4x2+4y2+8y+4... View Article
Inverse functions in trigonometry are used to get the angle with any of the trigonometry ratios. Cosine inverse is usually... View Article
A parabola is a graph that is U shaped. It is a conic section which is made by the intersection... View Article
XY plane in two dimensions is used to denote an ordered pair such as (x, y) in which former is... View Article
Derivative of the sum of two functions is the sum of their derivatives. The derivative of a sum of 2... View Article
The probability theory is a branch of Mathematics that deals with the chances of occurrence of the events. In probability... View Article
In diamond, the outer shell of each carbon atom has 4 electrons and again these electrons are shared with 4... View Article
Quadratic is relating to the second power. In Mathematics, the term quadratic describes something that pertains to terms of the... View Article
Complex numbers having the same real part and imaginary parts of opposite signs in a complex pair is defined as... View Article
‘Percent (%)’ means ‘out of one hundred’: To calculate 20% of number 50 Multiply 50 by 20%, and solve the... View Article
As per the definition of parallel lines, “parallel lines always maintain the same distance apart and never touch each other”.... View Article
Two lines are parallel if the length between two straight lines will be exactly the same at any point and... View Article
Parallel lines and curves are two different concepts. We can say two curves can be parallel. But can not describe... View Article
