Find real numbers a and b such that the equation (a- 2)+(b+5)i=14+19i is true.
a - 2 = 14
b + 5 = 19
To find the real numbers a and b that satisfy the equation, we can equate the real parts and the imaginary parts separately.
Let's equate the real parts:
(a - 2) = 14
To solve this equation, we can simply add 2 to both sides:
a = 14 + 2
a = 16
Now let's equate the imaginary parts:
(b + 5)i = 19i
From this equation, we can see that b + 5 = 19. To solve for b, we subtract 5 from both sides:
b = 19 - 5
b = 14
Therefore, the real numbers a and b that satisfy the equation are a = 16 and b = 14.
To find real numbers a and b that satisfy the equation, we need to equate the real and imaginary parts of the equation separately.
Let's equate the real parts:
a - 2 = 14
Solving for a:
a = 14 + 2
a = 16
Now, let's equate the imaginary parts:
b + 5 = 19
Solving for b:
b = 19 - 5
b = 14
Therefore, the real numbers a and b that satisfy the equation (a-2) + (b+5)i = 14 + 19i are a = 16 and b = 14.