Given two complex numbers

z₁ = a₁ + ib₁ and z₂ = a₂ + ib₂

        Then z₁+ z₂ = (a₁ + a₂) + i (b₁+b₂)

        And z₁ - z₂ = (a₁ - a₂) + i (b₁- b₂)

Example 1

Add the complex numbers

6+ 4i, 3 + 2i

Let z₁ = 6+ 4i, a₁ = 6, b₁ = 4

     z₂ = 3 +2i, a₂ = 3, b₂ = 2

Comparing with z₁ + z₂ = (a₁ + a₂) + i(b₁+ b₂)

                   6+ 4i + 3+ 2i = (6 + 3) + i (4 + 2)

                                         = 9 + 6i

Example 2

Add the complex numbers

-3-4i, 2+ 6i

Let z₁= -3- 4i, a₁= -3, b₁ = -4

     z₂= 2+ 6i,a₂ = 2,b₂ = 6

Comparing with z₁ + z₂ = (a₁+ a₂) +i (b₁+b₂)

                   -3-4i + 2 + 6i = (-3 + 2) + i (-4+ 6)

                                          = -1+2i

Example 3

Add the complex numbers

-5+ 6i, -5-6i

Let z₁= -5+ 6i, a₁= -5, b₁ = 6

      z₂= -5+ 6i, a₂ = -5,b₂ = -6

Comparing with z₁ + z₂ = (a₁+ a₂) +i (b₁+b₂)

                 (-5+ 6i) (-5-6i) = (-5 -5) +i (6- 6)

                                           = -10

Example 4

Add 4/3+2/7 i, - 11/2 - 5/6 i

Let z₁ = 4/3+2/7 i,   a₁= 4/3,    b₁= 2/7

     z₂ = - 11/2- 5/6 i, a₁= -, b₂= - 5/6

Comparing with z₁ + z₂ = (a₁+ a₂) +i (b₁+b₂)

   4/3+2/7 i - 11/2 - 5/6 i = (4/3 - 11/2 ) + i (2/7 - 5/6)

Example 5

Subtract 6+3i from 5+7i

Let z₁ = 5+7i, a₁= 5,  b₁=7s

     z₂ = 6+3i, a₂ = 6, b₂= 3

Comparing with z₁ - z₂ = (a₁- a₂) +i (b₁-b₂)

              (5+7i)- (6+3i) = (5-6) +i (7-3)

                                 = -1+ 4i

Example 6

Subtract - 506 + 217i from - 510 + 560i

Let z₁ = - 510 + 560 i, a₁= - 510,  b₁= 560

     z₂ = - 506 + 217i, a₂ = - 506, b₂= 217

     Comparing with z₁ - z₂ = (a₁- a₂) +i (b₁-b₂)

 (- 510 + 560i) - (- 506 + 217i)

                                      = (-510 - (-506) ) + i(560 - 217)

                                      = ( - 510+ 506) + i (343)

                                      = - 4+ 343i

Example 7

Subtract 12/7+ 17/4i from 2/3- 5/6i

Let z₁ = 2/3- 5/6i,        a₁= 2/3,   b₁= -5/6

     z₂ = 12/7+ 17/4 i,  a₂ =, b₂= 17/4

  Comparing with z₁ - z₂ = (a₁- a₂) +i (b₁-b₂)

(2/3 - 5/6 i) - (12/7 + 17/4 i) = (2/3 - 12/7) + i (- 5/6- 17/4)

Try these questions

1.    Add the following complex numbers

a.    -16+ 3i ; 7+ 4i

Answer: Let z₁ = -16+3i, a₁ = -16, b₁ =3

     z₂ = 7+4i,     a₂ = 7,    b₂= 4

Comparing with z₁ + z₂ = (a₁+ a₂) +i (b₁+b₂)

        (-16+3i) +(7+4i) = (-16 +7) +i (3+4)

                               = -9+7i

b.    

Answer:

c.    100 -14i; -6 -12i

Answer: 100 - 14i ; -6 -12i ;

Let z₁ = 100 -14i a₁= -100 b₁ = -14

     z₂ = -6 -12i       a₂ = -6     b₂= -12

Comparing with z₁ + z₂ = (a₁+ a₂) +i (b₁+b₂)

(100- 14i) + (-6-12i) = (100- 6) +i (-14-12)

                             = 94 - 26i

2.    Subtract the second number from the first number

a.    8 + 7i ; 6 - 41i

Answer: 8 + 7i; 6- 41i

Let z₁=8+ 7i       a₁= 8            b₁ =7

     z₂ = 6- 41i    a₂ = 6            b₂ = - 41

Comparing with z₁ - z₂ = (a₁- a₂) + i (b₁- b₂)

(8 + 7i) - (6 - 41i) = (8 - 6) + i (7 - (-41))

                         = 2 + i (7+ 41)

                         = 2 + 48i

b.    √7+ 13i ; 20 - 4√6 i

Answer: √7+ 13i; 20 - 4√6i

Let z₁ = √7+ 13i,      a₁ =,     b₁ = 13

      z₂ = 20 - 4√6i,     a₂ = 20,      b₂ = -4√6

Comparing with z₁ - z₂ = (a₁ - a₂) + i (b₁ - b₂)

( √7+ 13i) - (20 - 4√6i) = (√7 - 20) + i(13 - (-4√6))

= (√7 - 20) + (13 + 4√6)i

c.    - 9+ 10i ; -15 - 12i

Answer: -9 + 10i; -15 -12i

Let z₁=-9 +10i,     a₁= -9     b₁ =10

     z₂ = -15 –12i,  a₂ = -15   b₂ = -12

Comparing with z₁ - z₂ = (a₁- a₂) + i (b₁- b₂)

(-9 +10i)-(-15 - 12i) = (-9 - (-15) + i (10 - (-12))

                             = (-9 + 15) + i (10 + 12)

                             = 6 + 22i