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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)
If sin? = 1/2 , show that 3cos?-4cos 3 ? = 0. Ans: Sin ? = ½ ⇒ ? = 30 o Substituting in place of ? =30 o . We get 0.
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Determine that in a Boolean algebra, for any a and b, (a Λ b) V (a Λ b' ) = a. Ans: This can be proved either by using the distributive property of join over meet (or of mee
Quotient Rule : If the two functions f(x) & g(x) are differentiable (that means the derivative exist) then the quotient is differentiable and,
Consider a class of 55 students. The student names are placed in a hat & 3 names are randomly drawn without replacement. a) If the first person drawn was named the class presi
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Stratified sampling In stratified sampling case the population is divided into groups in such a way that units in each group are as same as possible in a process called strati
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Taylor Series - Sequences and Series In the preceding section we started looking at writing down a power series presentation of a function. The difficulty with the approach
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