Homework SourseIf z1 a a and where a is a real constant express z 1 and z
If z1 = a + a and where a is a real constant, express z _1 and z _2 in the form r cos theta and hence find an expression for (z power/ z power of 6 in terms of a and i. 
Solution
z1=a+a3i
z1=a(1+3i)
z1=2a((1/2)+(3 /2)i)
z1=2a cis(/3)
z2=1-i
z2=2((1/2)- (1/2)i)
z2=2 cis(7/4)
(z1/z2)=[2a cis(/3)]/[2 cis(7/4)]
(z1/z2)=[a2 cis((/3)-(7/4))]
(z1/z2)=a2 cis((-17/12))
(z1/z2)=a2 cis(2 +(-17/12))
(z1/z2)=a2 cis((7/12))
(z1/z2)6=(a2 cis((7/12)))6
(z1/z2)6=(a2)6 cis(6*(7/12)))
(z1/z2)6=8a6cis((7/2))
(z1/z2)6=8a6cis(2 +(3/2))
(z1/z2)6=8a6cis((3/2))
(z1/z2)6=8a6[cos((3/2))+i sin((3/2))]
(z1/z2)6=8a6[0+i(-1)]
(z1/z2)6=-8a6i
