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this question of engineering mathematics
Extracted text: Further problems 1 1 Simplify: (a) (5 + j4)(3 + j7)(2 -13) (2-13)(3 + j2) (4-13) 63 cos 3x +jsin 3x COSX +jsinx (b) (c) 2+j3 2 2 Express 4 I in the form a + jb. 3 If z express z in the form a+jb. 2+31-2 2+j 4 If find the real and imaginary parts of the complex number 5 Simplify (2+ jsj?, 5(7 + /2) 3-14 -(4- 16), expressing the result in the form a+ jb.
Extracted text: 12 Given that (a +b) +(a b) (1HA +i(2+D, obtain the values of a and b. 13 Express (-1+) in the form re where r is positive and -n<><. 14="" find="" the="" modulus="" of="" z="" -="" (2="" d(5="" +="" j12)/(1="" +="" 2).="" |15="" if="" x="" is="" real,="" show="" that="" (2="" +ell-dr="" +="" (2-del-x="" is="" also="" real.="" 16="" given="" that="" z="Rị" +r+="" jul;="" 2="Rai" z3="and" z4="R4" +c="" and="" also="" that="" zizs="2z4," express="" r="" and="" l="" in="" terms="" of="" the="" real="" constants="" r,="" r2,="" r4,="" cy="" and="" c.="" 17="" if="" z="x+iy," where="" x="" and="" y="" are="" real,="" and="" if="" the="" real="" part="" of="" (z="" +="" 1)/(2+)="" is="" equal="" to="" 1,="" show="" that="" the="" point="" z="" lies="" on="" a="" straight="" line="" in="" the="" argand="" diagram.="" 18="" when="" z="2" +="" 13,="" z2-3-14,="" z--5+="" j12,="" then="" e-="" iz,="" find="" e="" when="" i-5+="" j6.="" 19="" i="" r="" +hl="" if="" r2="" where="" r,="" r,="" rs,="" ra,="" w,="" l="" and="" c="" are="" real,="" show="" that="" r3="" cr="" r="" pcr+1="" 20="" if="" z="" and="" z="" are="" conjugate="" complex="" numbers,="" find="" two="" complex="" numbers,="" z="z" and="" z="2," that="" satisfy="" the="" equation:="" 32="" +="" 2(2-2)="" 39+j12="" on="" an="" argand="" diagram,="" these="" two="" numbers="" are="" represented="" by="" the="" points="" p="" and="" q.="" if="" r="" represents="" the="" number="" j1,="" show="" that="" the="" angle="" prq="" is="" a="" right="">