Why is the answer is zero in this complex (18-7i)+(20/7i)
To simplify the expression (18-7i) + (20/7i), we need to first rationalize the denominator of the second term.
The term (20/7i) can be rewritten as (20 * i) / (-7).
Then, adding the two complex numbers:
(18 - 7i) + (20 * i / -7)
To combine the real and imaginary parts separately:
Real part: 18 + (0) = 18
Imaginary part: -7 + (20/7) = (-49 + 20)/7 = -29/7
Therefore, the simplified expression is 18 - (29/7)i, which does not equal zero.
To find the sum of the complex numbers (18-7i) and (20/7i), we can add the real parts and the imaginary parts separately.
Given:
Complex number 1: 18 - 7i
Complex number 2: 20/7i
Real parts:
Real part of complex number 1: 18
Real part of complex number 2: There is no real part in the second complex number.
Imaginary parts:
Imaginary part of complex number 1: -7i
Imaginary part of complex number 2: 20/7i
Adding the real parts:
18 + 0 = 18
Adding the imaginary parts:
-7i + 20/7i
To add these imaginary parts, we need to get a common denominator, which is 7i. Thus, we multiply the numerator and denominator of the second term by i to make it 20i/7i:
(-7i + 20i) / 7i
Simplifying the numerator:
(-7i + 20i) = 13i
The sum of the imaginary parts is 13i.
Putting it all together:
The sum of the complex numbers (18-7i) and (20/7i) is:
18 + 13i
Therefore, the final answer is 18 + 13i.