Essential Mathematical Skills and Techniques-exercise semsister 1, Exercises of Mathematics

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3/14/25, 9:00 PM MAS152 - Semester 1 exercises MASI52 Essential Mathematical Skills & Techniques Examples 5: Complex Numbers 1 1, Express the following in the form z=a+ib (where aand b are real numbers) and write down the complex conjugate, modulus and principal argument of each of the resulting complex. numbers. (a) 3 + 4i) + 2 + 21) © Vi () @ +398 -2i) @ a+ira ~i) 2. Plot the following on the Argand diagram (@) 243i, ) 2-i, © 4-3, @ 342i 3. Given that x and y are real, write x yin iii in the form a+ib (where a and b are real). Hence find the values of x and y which satisfy the equation Tei 1-1 ° 4, Find the locus of the complex numbers z that satisfy [z+ 2i-3|=|z+ 3i Find the complex number that lies on this locus and has arg z= 7/4. 5. Find the roots of the equation P-(2 + i?+z-2 [Hint: look for an ‘obvious’ root.] Answers 1. @) 2=5 + 64, Z=5 ~6i, [z|=(2] ‘en ‘Argz = 0.8761, Argz () 2=12 + Si, Z=12 ~5i, |z|=[z)= 13, Arge = 0.3948, Argz= (©) z=-i, z=i, (Z| 1, Args (2, Argz = n/2 @ 2=-14i,7 zl=[z)= 2, Argz = 3n/4, Argz =—31/4, 3. Qx/5-y) + iG ~y-w/5);x= 5, y= 2. 4, Locus: y=-3x+ 2. 2=(1+ i/2 5. 2+i, 41 about:blank 1/46