By K. A. Stroud

Because the e-book of the 3rd version of "Engineering Mathematics", substantial alterations in syllabuses and strategies for a degree skills in arithmetic were brought nationally, due to which scholars with quite a few degrees of mathematical heritage were enrolling for undergraduate classes in engineering and technology. those adjustments have result in the necessity for studying fabrics aimed toward various degrees. this article hence contains ten programmes which act as an creation to "Engineering arithmetic" and is designed for these scholars impending the topic for the 1st time.

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**Extra resources for Engineering Mathematics: Programmes and Problems**

**Sample text**

You no doubt have hazy recollections of these series You had better make a note of them since they have turned up. 27 Complex numbers 1 If we now take the series for ex and write j8 in place of x, we get eje 54 = 1 + j8 + (j8)2 + (j8)3 + (j8)4 + 1== 1 +j8 + 2! - . ()2 - 2! - ()2 (}4 - 1 + ]8 4! 3! 2! -2 8 2 -3 8 3 + 1- 3! j83 ·4e4 + 1- 4! + .. - 83 85 . :::: cos e + j sin .. ) e Therefore, r(cos 8 + j sin 8) can now be written as reje. This is called the exponential form of the complex number.

If Z = -5 + j2, r = y(25 + 4) = y29 = 5-385 and from above () = 158°12' The full polar form is z = 5-385 (cos 158°12' + j sin 158°12') and this can be shortened to z = 5-385 1158°12' Express in shortened form, the polar form of (4- j3) Do not forget to draw a sketch diagram first. 24 Programme 1 48 X r=v(4 2 +3 2 ) r=5 tan E =0·75 :. E =36°52' :. 8 = 360° - E = 323°8' :. z =5(cos 323°8' + j sin 323°8') = 5 1323°8' 00000000000000000000000000000000000000 Of course, given a complex number in polar form, you can convert it into the basic form a + jb simply by evaluating the cosine and the sine and multiplying by the value of r.

Express (-1 + j) in the form r ej 8 , where r is positive and -7r < e < 1T. 14. Find the modulus of z = (2- j) (5 + j 12)/{1 + j2) 3 • 15. lfx is real, show that (2 + j)e(t+j 3 )x + (2- j)e< 1-j 3 )x is also real. 16. Given that z 1 =R 1 + R + jwL; z2 =R 2 ;z 3 = ~C; and JW 3 z 4 = R 4 + ~C ;and also that z 1z 3 = z 2 z 4 , express Rand Lin terms JW 4 of the real constants R 1, R 2 , R 4 , C3 and C4 . 17. If z = x + jy, where x andy are real, and if the real part of (z + 1)/(z + j) is equal to 1, show that the point z lies on a straight line in the Argand diagram.