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mathsComplex NumbersAlgebra of Complex Numbers

### Subtraction of Complex Numbers

Complex numbers subtraction is explained

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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).

Complex number Subtraction:
z_1-z_2
quad quad =a_1+ib_1 - (a_2+ib2)
quad quad =a_1-a_2+ib_1-i_b2 (associative law)
quad quad = a_1-a_2+ i(b_1-b2) (distributive law)
quad quad =(a_1-a_2) + i (b_1-b_2) (real and imaginary parts of result)

Subtraction of two complex numbers is the subtraction of real and imaginary parts individually.

Subtraction 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 z_1 = 2.1+i and z_2 = -2.1+i What is z_1-z_2?

• 4.2+2i
• 4.2
• 4.2
• 4.2-2i
• -4.2+2i