The distance betwen points a = 1 + 1i and b = a + b is 5. find the point b for each value provided below.
a. a = 4
b. b = 6

(a) 4+5i or, 4-3i

(b) 1+6i

Step-by-step explanation:

The distance between the points A= 1+i, and B=a+bi is 5.

Therefore, we can write

⇒ ..... (1)

(a) If the value of a is 4, then from equation (1), we get

(4-1)²+(b-1)² = 25

⇒ (b-1)² =16  

⇒ b-1 =±4

⇒ b= 5 or -3

Therefore, the point B will be represented by 4+5i or, 4-3i (Answer)

(b) If the value of b is 6, then from equation (1), we get

(a-1)²+(6-1)² = 25

⇒ (a-1)² =0  

⇒ a = 1

Therefore, the point B will be represented by 1+6i. (Answer)

d. 8

step-by-step explanation:

the given radical expression is:

we can rewrite this as:

we express as square numbers to get;

the exponents will now cancel out to give.

the correct answer is d