Write a quotient 10/1+2i in the form a+bi I need help 20 points

The quotient 10/1+2i in the form a+bi is; 2-4i

According to the question;

To convert the expression to the form; a+bi.

We can do the following;

Multiply both the numerator and denominator by (1-2i); so that we have;

where i² = -1

Therefore, we have;

Read more on complex numbers;

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2 - 4i

Step-by-step explanation:

Given the complex number  10/1+2i, to write this in the form a + bi, we will rationalize the function as shown;

= 10/1+2i * 1-2i/1-2i

= 10(1-2i)/(1+2i)(1-2i)

= 10-20i/(1-2i+2i-4i²)

= 10-20i/1-4(-1)

= 10-10i/1+4

= 10-20i/5

= 10/5 - 20i/5

= 2 - 4i

Hence the expression in the form a + bi is 2 - 4i

hello from mrbilldoesmath!

answer:   (7x + 6y) ( 49x^2 - 42xy + 36y^2)

discussion:

in general, the factorization of a^3 + b^3 is

a^3 + b^ 3 = (a + b) ( a^2 - ab + b^2)

in our case note that 343 = 7^3 and 216 = 6^3 so the equation becomes:

343x^3 + 216y^3 = (7x)^3 + (6y)^3

if you think of a (above) as 7x and b as 6y the factorization becomes

343x^3 + 216y^3 =

((7x + 6y) (   (7x)^2 - 7x*6y + (6y)^2)   =

(7x + 6y) ( 49x^2 - 42xy + 36y^2)

you,

mrb

(a + b) (a^2 - a b + b^2)