Obtain the polar and exponential representations of z₁, z₂ and z₁z₂, where z1 = 1/2 - i and z₂ = 3+i
हम दिए गए संख्याओं \( z_1 = \frac{1}{2} - i \) और \( z_2 = 3 + i \) का ध्रुवीय (Polar) और घातांक (Exponential) रूप निकालेंगे। ### 1. ध्रुवीय रूप (Polar Representation) ध्रुवीय रूप के लिए, किसी भी जटिल संख्या \( z = a + ib \) को इस रूप में लिखा जाता _____ _____ ________ _____ __________ _____ ______ _______.
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Which of the following statements are true? Justify your answers. (This means that if you think a statement is false, give a short proof or an example that shows it is false. If it is true, give a short proof for saying so. For instance, to show that '{1, padma, blue} is a set' is true, you need to say that this is true because it is a well-defined collection of 3 objects.)
i) The collection of Venn diagrams is a set.
ii) (A\B) UC=A\(B∩C) for any three sets A, B and C.
iii) If ze R, then |z|=z.
iv) xm + a1 xm -1+ ....am-1 x + am = 0, ai ∈ R∀ i = 1, ..., m, has a root in R only if m is an odd number.
v) x > 0 is necessary for x+3>1.
vi) Any system of three linear equations in two variables has no solution.
vii) If a matrix has n² entries, where n∈ N, then it is a square matrix.
viii) For n > 4, the AM of the first n natural numbers is greater than n +1.
Find the polynomial over R of least degree which has as its roots. as its roots.
egers Write an odd natural number as a sum of two int m and 1 m in a way that 2 m is maximum.
Find x and y, given that (5x + y, 3x - y) = (2, 2x)∈QxQ.
Express z = 2/-4-i in standard (algebraic) form. Further, give an Argand diagram in which z, Z and -z are plotted.
क्या नीचे दिए रैखिक निकाय को हल करने के लिए क्रेमर नियम लागू होता है? यदि हाँ, तो इसका प्रयोग कीजिए। अन्यथा निकाय के अंतिम समीकरण को बदल दीजिए, ताकि निकाय का हल इस नियम से प्राप्त हो जाए।
Is Cramer's Rule applicable for solving the linear system below? If yes, apply it. Otherwise, alter the last equation in the system so that the solution can be obtained by applying the Rule.