Question

If ((3+2i/2-3i) + (5-i/2+3i)) * a/b, then a=? and b=?

Answer 1

`a=13\\ \\b=7-4i`

Explanation:

Consider the expression in the brackets:

`(3+2i)/(2-3i)+(5-i)/(2+3i)`

Simplify it:

`(3+2i)/(2-3i)+(5-i)/(2+3i)\\ \\=((3+2i)(2+3i)+(5-i)(2-3i))/((2-3i)(2+3i))\\ \\=(6+9i+4i+6i^2+10-15i-2i+3i^2)/(2^2-(3i)^2)\\ \\=(16-4i+9i^2)/(4-9i^2)\\ \\=(16-4i-9)/(4-9(-1))\\ \\=(7-4i)/(13)`

So,

`a=13\\ \\b=7-4i`