Friday

January 30, 2015

January 30, 2015

Posted by **Maria** on Sunday, November 3, 2013 at 10:40pm.

and

write 1+4i over 1-i in the form a+bi

- Math -
**Jai**, Sunday, November 3, 2013 at 10:55pm#1.

I'm not sure if you mean x - sqrt(x-2) = 4 or x - sqrt(x) - 2 = 4, but I'll go with the first.

x - sqrt(x-2) = 4

To do this, we isolate the term with squareroot to one side of equation:

x - 4 = sqrt(x-2)

Then we square both sides and solve for x:

(x - 4)^2 = (sqrt(x-2))^2

x^2 - 8x + 16 = x - 2

x^2 - 8x - x + 16 + 2 = 0

x^2 - 9x + 18 = 0

(x - 6)(x - 3) = 0

x = 6 and x = 3

We need to check these values of x by substituting them back to the original:

x = 6 :

6 - sqrt(6-2) = 4

6 - sqrt(4) = 4

6 - 2 = 4

4 = 4

Thus x is indeed equal to 6.

x = 3 :

3 - sqrt(3-2) = 4

3 - sqrt(1) = 4

3 - 1 = 4

2 =

Thus x is NOT equal to 3.

#2.

(1 + 4i) / (1 - i)

Multiply both numerator and denominator by the conjugate of denominator:

= (1 + 4i) / (1 - i) * (1 + i)/(1 + i)

= (1 + 4i + i + 4i^2) / (1 - i^2)

Note that i^2 = -1, thus

= (1 + 5i + 4(-1)) / (1 -(-1))

= (1 + 5i - 4) / 2

= -3/2 + (5/2)i

Hope this helps :3

**Answer this Question**

**Related Questions**

algebra 2 - Would some one look at these problems and see if I got them right ...

Math help, anyone? - Solve the proportion. Where necessary, round to the nearest...

Algebra 2 - would some one please check these for me 1. divide x^2-36y^2 over 5x...

math - how can you find 11 over 12 - 2 over 3 write the difference in simplest ...

math - Perform the operation and write the result in standard form. 1 + i over i...

Math plz help me!!! URGENT!! - 1. Write the ratio in the simplest form. 16:24 (1...

Math Quiz - Math Quiz please help fast Write the following ratio in simplest ...

7th grade math help please the REAL ms.sue - 1. Mac’s farm has a total of 18 ...

art - The statement "form follows function" means function over form, form over ...

7th grade math standard form scientific notation - In standard form: 5. 3.2 x 10...