Find the complex (18-7i) + (20÷7i)
To add complex numbers, we add the real parts separately and the imaginary parts separately.
The real part of (18 - 7i) is 18, and the real part of (20 ÷ 7i) is 0.
18 + 0 = 18.
The imaginary part of (18 - 7i) is -7, and the imaginary part of (20 ÷ 7i) is 20 ÷ 7.
-7 + 20 ÷ 7 = -7 + 2.8571 ≈ -4.1429.
Therefore, (18 - 7i) + (20 ÷ 7i) = 18 - 4.1429i.
To find the sum of the complex numbers (18 - 7i) and (20 ÷ 7i), we can simplify the expression by converting the division into multiplication with the conjugate.
Step 1: Simplify the expression (20 ÷ 7i) by multiplying the numerator and denominator by the conjugate of the denominator, which is -7i.
(20 ÷ 7i) × (-7i ÷ -7i) = (-140i ÷ -49)
Step 2: Combine the two complex numbers.
(18 - 7i) + (-140i ÷ -49)
Step 3: Distribute the division to both terms inside the parentheses.
(18 - 7i) + (-140i) ÷ (-49)
Step 4: Rewriting the division as multiplication by the reciprocal.
(18 - 7i) + (-140i) × (-1/49)
Step 5: Simplify the multiplication.
(18 - 7i) + (140i/49)
Step 6: To add the two complex numbers with different real and imaginary parts, combine the real parts and imaginary parts separately.
Real part: 18 + 0 = 18
Imaginary part: -7i + (140i/49)
Step 7: Combine the like terms in the imaginary part.
-7i + (140i/49) = (49*(-7i) + 140i)/49 = (-343i + 140i)/49 = (-203i)/49
Therefore, the sum of the complex numbers (18 - 7i) and (20 ÷ 7i) is:
18 - (203i)/49