Calculate and write result in a+bi form.
5+10i/3-4i
multipy the numberator and denominator by the denominator's conjugate.
(5+10i)(3+4i)/(9+16)=(15+30i+20i-40)/25
simplify
To calculate the result in the form a+bi, where a and b are real numbers, we can use the concept of complex conjugates.
To begin with, we need to multiply the numerator and denominator by the complex conjugate of the denominator. The complex conjugate of a complex number is obtained by changing the sign of its imaginary part.
Given the expression (5+10i) / (3-4i), the complex conjugate of the denominator (3-4i) is (3+4i).
Now let's multiply the numerator and denominator by the complex conjugate:
[(5+10i) * (3+4i)] / [(3-4i) * (3+4i)]
Expanding the numerator and denominator:
(5 * 3) + (5 * 4i) + (10i * 3) + (10i * 4i) / (3 * 3) + (3 * 4i) - (4i * 3) - (4i * 4i)
Simplifying:
15 + 20i + 30i + 40i^2 / 9 + 12i - 12i - 16i^2
Now let's simplify further:
15 + 20i + 30i - 40 / 9 + 16
Combine like terms:
-25 + 50i / 25
Simplifying fractional division:
-1 + 2i
Therefore, the result of (5+10i) / (3-4i) in the form a+bi is -1+2i.