Let the given complex number
z = x + ix =
We have to find the standard form of complex number.
Solution:
∴ x + iy =
Rationalising numerator part of complex number, we get
x + iy =
⇒ x + iy =
Using the algebraic identity:
(a + b)(a - b) = -
⇒ x + iy =
⇒ x + iy = [ ∵
]
⇒ x + iy =
⇒ x + iy =
⇒ x + iy =
⇒ x + iy = 1 - i
Thus, the given complex number in standard form as "1 - i".
Answer:
The answer is: 13 minutes
Step-by-step explanation:
First Let us form equations with the statements in the two scenario
Let the time in which the bell rings be 'x'
1. If Andrew walks (50 meters/minute), he arrives 3 minutes after the bell rings. Therefore the time of arrival at this speed = (3 + x) minutes
2. If Andrew runs (80 meters/minute), he arrives 3 minutes before the bell rings. Therefore the time taken to travel the distance = (x - 3) minutes
In both cases, the same distance is travelled, therefore, equation (1) = equation (2)
Next, collecting like terms:
dividing both sides by 3:
x = 390÷30 = 13
∴ x = 13 minutes