Question

2+6i/2-4i = a + bi What is the value of a? What is the value of b?

Answer 1

To solve the expression 2+6i/2-4i = a + bi, we can multiply the numerator and denominator by the conjugate of the denominator and simplify to find that the value of a is 5/3 and the value of b is -5/3.

Step-by-step explanation:

To solve the expression 2+6i/2-4i = a + bi, we can multiply the numerator and denominator by the conjugate of the denominator, which is 2+4i. This will eliminate the imaginary part in the denominator.

Multiplying the numerator and denominator by 2+4i, we get ((2+6i)*(2+4i))/((2-4i)*(2+4i)).

Expanding and simplifying this expression, we get (4+8i+12i-24)/(4+8i-8i-16) = (4+20i-24)/(4-16) = (-20+20i)/(-12) = (20/12)-(20/12)i = 5/3 - (5/3)i.

Therefore, the value of a is 5/3 and the value of b is -5/3.

Answer 2

`(2+6i)/(2-4i)\\\\\\=(2(1+3i))/(2(1-2i))\\\\\\=(1+3i)/(1-2i)\\\\\\=((1+3i)(1+2i))/((1-2i)(1+2i))\\\\\\=(1+2i+3i+6i^2)/(1-(2i)^2)\\\\\\=(1+5i-6)/(1+4)~~~~;[i^2=-1]\\\\\\=(5i-5)/(5)\\\\\\=\frac{5(i-1)}5\\\\=i-1\\\\=-1+i\\\\\text{It is in a form of a +bi so,}~ a = -1~ \text{and}~ b = 1`