+101 For complex number z, what is 2z + i = iz + 3?
(Please respond in form x + yi)
Thanks for your time!
+128408 2z + i = iz + 3
2 (a + bi) + i = i ( a + bi) + 3
2a + 2bi + 1i = ai - b + 3
Equating real and complex parts
2a = 3 - b ⇒ 2a + b = 3 ⇒ 4a + 2b = 6 (1)
(2b + 1) = a ⇒ a - 2b = 1 ⇒ a - 2b = 1 (2)
Add (1) and (2) and we get that
5a = 7
a = 7/5
And
2(7/5) + b = 3
14/5 + b = 15/5
b = 15/5 - 14/5
b = 1/5
So
z = a + bi
z = (7/5) + (1/5) i
