Answer:
Question (5):
[tex](2x - y) + (x - 2y)i = 5 + i \\ \\ 2x - y + xi - 2yi = 5 + i [/tex]
• group imaginary terms and real terms on different sides:
[tex]2x - y - 5 = i - xi + 2yi \\ \\ 2x - y - 5 = (1 - x + 2y)i[/tex]
• To find value of x, Imaginary part is zero
[tex]2x - y - 5 = 0 \\ 2x - y = 5 - - - (a)[/tex]
• For Imaginary part, real part is zero:
[tex]1 - x + 2y = 0 \\ x - 2y = 1 - - - (b)[/tex]
• solving simultaneously:
[tex]{ \boxed{ \boxed{ \: \: x = 3 \: \: }}} \: and \: { \boxed{ \boxed{ \: \: y = 1 \: \: }}}[/tex]
Question (4):
[tex](2x - 3) + (3y + 1)i = 7 + 10i \\ \\ 2x - 3 + 3yi + i = 7 + 10i \\ \\ 2x - 3 - 7 = 10i - 3yi - i \\ \\ 2x -10 = (9 - 3y)i[/tex]
• Group imaginary part and real part
[tex]2x - 10 = 0 \\ 2x = 10 \\ { \boxed{ \: \: x = 5 \: \: }}[/tex]
for y:
[tex]9 - 3y = 0 \\ 3y = 9 \\ { \boxed{ \: \: y = 3 \: \: }}[/tex]
