Question

IF Z,=2+31, 2q = 1-2i, Find the value of zı+322, 2,022
$if z1 = 2 + 3i z2 = 1 - 2i find the value of z1 + 3z2$
​

Answer 1

z

1

=2−i⇒

z

1

ˉ

=2+i,z

2

=−2+i

(i) z

1

z

2

=(2−i)(−2+i)=−4+2i+2i−i

2

=−4+4i−(−1)=−3+4i

∴

z

1

ˉ

z

1

z

2

=

2+i

−3+4i

=

(2+i)(2−i)

(−3+4i)(2−i)

=

2

2

+1

2

−6+3i+8i−4i

2

=

2

2

+1

2

−6+11i−4(−1)

=

5

−2+11i

=

5

−2

+

5

11

i

∴Re(

z

1

ˉ

z

1

z

2

)=

5

−2

(ii)

z

1

z

1

ˉ

1

=

(2−i)(2+i)

1

=

(2)

2

+(1)

2

1

=

5

1

∴Im(

z

1

z

1

ˉ

1

)=0