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For complex number z, the minimum value of |z| + |z - cosa - i sina|+|z - 2(cosa + i sina )| is..? Solution) |z| + |z-(e^ia)| + |z-2(e^ia)| we see.....oigin , e^ia , 2e^ia , forms a straight line.and for minimum value..... z must coincide with e^iahence the equation becomes:=|e^ia| + 0 + |-e^ia|=1 + 0 + 1=2(ANS)
lim n tends to infintiy ( {x} + {2x} + {3x}..... +{nx}/ n2(to the square) )where {X} denotes the fractional part of x? Ans) all no.s are positive or 0. so limit is either positive
9x-5x+2 and y=4x+12
A straight line AB on the side of a hill is inclined at 15.0° to the horizontal. The axis of a tunnel 486ft. long is inclined 28.6° below the horizontal lies in a vertical plane wi
20% of the total quantity of oil is 40 litres find the total quantity of oil in litres
If the following terms form a AP. Find the common difference & write the next 3 terms3, 3+ √2, 3+2√2, 3+3√2.......... Ans: d= √2 next three terms 3 + 4 √ 2 , 3 + 5√ 2 ,
Verify Liouville''s formula for y^ prime prime prime -y^ prime prime - y'' + y = 0 in [0, 1]
Explain how we Converting Fractions to Percents ? To convert a fraction to a percent: 1. Convert the fraction to a decimal using long division. 2. Move the decimal point two p
E1) Create a guessing game for children of Class 2, to familiarise them with the concept of a time interval E2) How could you use group dancing to teach concepts of geometry? Th
The F Distribution The F distribution is the distribution of the ratio of 2 random variables. Both random variables have yet another distribution, called the c 2 Distri
(a+b)''2
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