Simplify 4-7i/2+5i
4+3i/2
To simplify the expression (4-7i)/(2+5i), we can use the concept of complex conjugates.
The complex conjugate of a complex number a+bi is denoted as a-bi, where a and b are real numbers. In other words, we change the sign of the imaginary part.
To simplify the expression, we need to eliminate the complex number in the denominator by multiplying both the numerator and the denominator by the conjugate of the denominator, which is 2-5i.
So, we have:
(4-7i)/(2+5i) * (2-5i)/(2-5i)
To multiply complex numbers, we can use the FOIL method, which stands for First, Outer, Inner, and Last.
First: (4)(2) = 8
Outer: (4)(-5i) = -20i
Inner: (-7i)(2) = -14i
Last: (-7i)(-5i) = 35
Combine the results:
8 + (-20i) + (-14i) + 35 = 43 - 34i
Therefore, the simplified form of (4-7i)/(2+5i) is 43 - 34i.
I am sure you meant:
(4-7i)/(2+5i)
= (4-7i)/(2+5i)*(2-5i)/(2-5i)
= (8 -20i - 14i + 35i^2 )/(4 - 5)
= 8 - 34i - 35)/-1
= 27 + 34i