Question

26. If z1 = a + ib and z2 = c + id, be any two
complex numbers. Then the sum z1 + Z2 be
(2 Points)
a + b
а+ С
(a + c) + i(b + d)
none of these​

Answer 1

Answer:

z

1

=a+ib∣z

1

∣=1

z

2

=c+id∣z

2

∣=1

Re(z

1

z

2

ˉ

)=0

z

1

=a+ib=cis(A)=cosA+isinA ..{∵∣z

1

∣=1}

z

2

=c+id=cis(B)=cosB+isinB ...{∵∣z

2

∣=1}

⟹a=cosA&b=sinA

Re(cis(A)cis(−B))=0

⟹cos(A−B)=0

⟹A−B=

2

π

⟹z

2

=cos(A−

2

π

)+isin(A−

2

π

)=sinA−icosA

⟹c=sinA&d=−cosA

w

1

=a+ic=cosA+isinA=cisA

w

2

=b+id=sinA−icosA=−i(isinA+cosA)=−icis(A)

⟹∣w

1

∣=1&∣w

2

∣=1

w

1

w

2

ˉ

=icisAcis(−A)=i

⟹Re(w

1

w

2

ˉ

)=0