Mathematics: Given that [tex]z=x+iy[/tex], find the value of x and of y such that [tex]z+4iz^*=-3+18i[/tex] where z* is the complex conjugate of z.

Given that [tex]z=x+iy[/tex], find the value of

Ответ:

andrew5182

02.01.2022

Mathematics

z= 5-2i

Step-by-step explanation:

Start replacing!

$(x+iy) + 4i (x-iy) = -3+18i \\ x+iy +4ix -4i^2 y = -3 + 18i \\\\x + i (4x+y) +4y = -3 + 18i\\x+4y + (4x+y) i = -3 + 18i$

Now two complex numbers are equal if both the real and imaginary parts are equal, which gives you the system of equation $\left \{x+4y=-3} \atop {4x+y=18} \right.$

Pick any method to solve it and you'll get x=5, y= -2

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Ответ:

Kylabayor

28.06.2021

Mathematics

$\frac{2}{4^-3} \\ \\ \frac{2}{ \frac{1}{4^3} } \\ \\ \frac{2}{ \frac{1}{64} } \\ \\ 2 \times 64 \\ \\ 128 \\ \\ \fbox {128}$

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Given that $z=x+iy$ , find the value of x and of y such that $z+4iz^=-3+18i$ where z is the complex conjugate of z.

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Given that , find the value of x and of y such that where z* is the complex conjugate of z.

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Given that $z=x+iy$ , find the value of x and of y such that $z+4iz^=-3+18i$ where z is the complex conjugate of z.