Answer:
(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 [tex]\sqrt{(a-1)^{2} +(b-1)^{2} } =5[/tex]
⇒[tex](a-1)^{2} +(b-1)^{2} =25[/tex] ..... (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)
