How to multiply and divide complex numbers?

I need help multiplying these complex numbers:


(4+2i)(1-5i)





And dividing these:


(6-3i)/(2+i)





Thanks!How to multiply and divide complex numbers?
You have to FOIL to mult. them.


F-4


O-20i


I- 2i


L- -10i^2


The i^2 becomes a -1, so the L becomes 10


When simplified it becomes 14+22i





To divide you have to multi. both the top and bottom with (2-i)


then you FOIL them.





The final answer is 15+3i/5





Hope this helpsHow to multiply and divide complex numbers?
It's just as if ';i'; was a variable like ';x';. Just treat ';i'; as if it were any other variable.





(4 + 2i)(1 - 5i) = 4 - 18i - 10i^2


Now, keep in mind that, by the definition of ';i';, i^2 = -1


So, 10i^2 = -10


And your product is:


4 - 18i - (-10), which simplifies to:





16 - 18i, which is your answer.








The second one is easier; just pretend that ';i'; is any variable. If you factor (6 - 3i), you get:


(6 - 3i) = 3(2 - i)


So, (6 - 3i) / (2 - i) = 3(2 - i) / (2 - i), which is equal to 3.





Answer is 3.
multiply using foil


4-20i+2i-10i^2


4-18i-10(-1)


4-18i+10


14-18i





divide


(6-3i)/(2+i)


1.8-2.4i