Final answer:
To divide the complex number 7+6i by 8-2i, you multiply both the numerator and the denominator by the conjugate of the denominator, which is 8+2i. This process turns the division into multiplication and results in a real number for the denominator.
Step-by-step explanation:
The division of 7+6i over 8-2i is performed by multiplying the numerator and denominator by the conjugate of the denominator, which in this case is 8+2i. Multiplying both the numerator and denominator by the conjugate is done to eliminate the imaginary part from the denominator, resulting in a real number. By performing this multiplication, one is essentially converting the original division problem into a multiplication problem that simplifies to a form where the denominator becomes a real number.
To calculate the division of complex numbers in the form of a+bi and c+di, you first multiply both the numerator (a+bi) and the denominator (c+di) by the conjugate of the denominator (c-di). When you do this, the denominator becomes a real number as (c+di)(c-di) = c²+d². Then you'll have a new fraction with a real denominator which can be simplified further.