# ADDING SUBTRACTING MULTIPLTYING COMPLEX NUMBERS

Complex number will consists of two parts,

(i) Real part

(ii) Imaginary part

General form of complex number is a + ib

Here a is real and b is imaginary.

How to add complex numbers ?

Consider two complex numbers,

Let z1 = a + ib and z2 = c + id

z+ z2 = a + ib + c + id

= (a + c) + ib + id

= (a + c) + i(b + d)

Combining the real parts and combining imaginary parts.

How to subtract complex numbers ?

Consider two complex numbers,

Let z1 = a + ib and z2 = c + id

z+ z2 = a + ib - (c + id)

= (a + c) - ib - id

= (a + c) - i(b + d)

Combining the real parts and combining imaginary parts.

How to multiply complex numbers ?

Consider two complex numbers,

Let z1 = a + ib and z2 = c + id

zz2 = (a + ib)(c + id)

= ac + iad + ibc + i2bd

= ac + iad + ibc + (-1)bd

= ac - bd + i(ad + bc)

Simplify :

Problem 1 :

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

Solution :

= (-3 + 4i) + (-4 + 7i)

= (-3 – 4) + 4i + 7i

= -7 + 11i

Problem 2 :

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

Solution :

= 3 - 6i + 7 + 3i

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

= 10 - 3i

Problem 3 :

(3 + 8i) + (1 - i)

Solution :

= (3 + 1) + (8i – i)

= 4 + 7i

Problem 4 :

(4 - 4i) + (-4 + 6i)

Solution :

= 4 - 4 - 4i + 6i

= 2i

Problem 5 :

-6i + (3i) - (-7 - 8i)

Solution :

= (-6i) + (3i) - (-7 - 8i)

Distributing negative, we get

= (-6i) + (3i) + 7 + 8i

= -6i + 3i + 8i + 7

= 5i + 7

Problem 6 :

(-5 - 3i) - (8 + i)

Solution :

= (-5 - 3i) - (8 + i)

= -5 - 3i - 8 - i

= -5 - 8 - 3i - i

-13 – 4i

Problem 7 :

(8 - 5i) - (-4 - 3i)

Solution :

(8 - 5i) - (-4 - 3i)

= 8 - 5i + 4 + 3i

= 12 – 2i

Problem 8 :

-4 + (7i) - (1 - 5i)

Solution :

-4 + (7i) - (1 - 5i) = (-4 – 1) + (7i – (-5i))

= -5 + 12i

Problem 9 :

(-6 – 6i) – (2 – 2i)

Solution :

(-6 – 6i) – (2 – 2i)

= -6 - 2 - 6i + 2i

= -8 – 4i

Problem 10 :

(-3i) – (-5 + 7i) + i

Solution :

= (-3i) – (-5 + 7i) + i

= -3i + 5 - 7i + i

= -9i + 5

Problem 11 :

(8i) (-6i) (-3i)

Solution :

(8i) (-6i) (-3i)

= -48i2(-3i)

= 144 i2 i

= 144(-1) i

= -144 i

Problem 12 :

(2i) (3i) (-6i)

Solution :

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

= 6i2 (-6i)

= -36 (i2) i

= -36(-1) i

= 36i

## Recent Articles

1. ### Finding Range of Values Inequality Problems

May 21, 24 08:51 PM

Finding Range of Values Inequality Problems

2. ### Solving Two Step Inequality Word Problems

May 21, 24 08:51 AM

Solving Two Step Inequality Word Problems