Question

find the product and quotient of the complex numbers 1+i and 3+i​

Answer 1

Answer:

to find product of 1 + i and 3 + i

and quotient of 1 + i and 3 + i

Step-by-step explanation:

product => (1 + i)(3 + i)

=> 3 + i + 3i + i²

=> 3 + 4i - 1 [ i = √-1 hence i² = -1 ]

=> 2 + 4i Answer part 1

quotient => 1 + i / 3 + i

multiply both number and denominator by the conjugate of the denominator ie 3 - i

=> (1 + i)(3 - i) / (3 + i)(3 - i)

=> (3 - i + 3i - i²) / (9 + i²) [ (a-b)(a+b) = a²-b² ]

=> [3 + 2i - (-1)] / [9 + (-1)]

=> (4 + 2i) / 9 - 1

=> 4 + 2i / 8

=> 2 ( 2 + i) / 8

=> (2 + i) / 4 => Answer part 2