Multiply and Divide Complex Numbers

Multiplication of Complex Numbers

The product of complex numbers a + bi and c + di is given as:

(a + bi) + (c + di) = (ac – bd) + (ad + bc)i

Example:

(4 – 2i)(3 + 5i) = 4(3 + 5i) – 2i(3 + 5i)                           (Using distributive property over addition)

= 12 + 20i – 6i – 10i² = 12 + 20i – 6i + 10                   (As i² = -1)

= 22 + 14i                                                                                 (Grouping like terms)                

Division of Complex Numbers                                                  

Multiply both numerator and denominator by conjugate of denominator and simplify

Example:

 

 

 

 

 

 

 

 

 

 

 

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