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mathsComplex NumbersAlgebra of Complex Numbers

### Addition of two Complex numbers

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Consider two complex numbers z_1=a_1+ib_1 and z_2 = a_2+ib_2. What is z_1+z_2?

• (a_1+a_2) + i (b_1+b_2)
• (a_1+a_2) + i (b_1+b_2)
• a_1+ib_1
• a_2+ib_2

The answer is '(a_1+a_2) + i (b_1+b_2)'. This is from the associative and distributive laws of real numbers extended to numbers with sqrt(-1).

z_1+z_2
quad quad =a_1+ib_1 + a_2+ib_2
quad quad =a_1+a_2+ib_1+ib_2 (associative law of addition)
quad quad = a_1+a_2+ i(b_1+b_2) (distributive law of multiplication over addition)
quad quad =(a_1+a_2) + i (b_1+b_2) (real and imaginary parts of result)

Addition of two complex numbers is the addition of real and imaginary parts individually.

Addition of Complex numbers : For any complex number z_1=a_1+ib_1 in CC and z_2 = a_2+ib_2 in CC
z_1+z_2 = (a_1+a_2)+i(b_1+b_2)

Solved Exercise Problem:

Given two complex numbers 3+2i and -1+i, what is the sum?

• 3+i
• 2+3
• 2+3i
• 2+3i
• 2-i

The answer is '2+3i'

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