Let
z=x+iy⇒z∗=x−iyz = x + iy \Rightarrow z* = x - iyz=x+iy⇒z∗=x−iy
Then
2(x+iy)−i(x−iy)=3(3−5i)2x+2iy−ix+i2y=9−15i2x−y+i(2y−x)=9−15i\begin{array}{l} 2(x + iy) - i(x - iy) = 3(3 - 5i)\\ 2x + 2iy - ix + {i^2}y = 9 - 15i\\ 2x - y + i(2y - x) = 9 - 15i \end{array}2(x+iy)−i(x−iy)=3(3−5i)2x+2iy−ix+i2y=9−15i2x−y+i(2y−x)=9−15i
{2x−y=92y−x=−15\left\{ \begin{array}{l} 2x - y = 9\\ 2y - x = - 15 \end{array} \right.{2x−y=92y−x=−15
{2x−y=93x=3\left\{ \begin{array}{l} 2x - y = 9\\ 3x = 3 \end{array} \right.{2x−y=93x=3
{x=1y=−7\left\{ \begin{array}{l} x = 1\\ y = -7 \end{array} \right.{x=1y=−7
Answer: z=1−7iz = 1 - 7iz=1−7i
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