What is the answer to 4(x-yi)=8+2yi+10i ?

The answer to 4(x-yi)=8+2yi+10i is x=2,y=-5/3

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4(x-yi)=8+2yi+10i

4 (x - y i) = 8 + 2 y i + 10 i

x = 2, y = - \frac{5}{3}

Solution steps

4 (x - y i) = 8 + 2 y i + 10 i

Rewrite

4 (x - y i)

in standard complex form:

4 x - 4 y i

4 x - 4 y i = 8 + 2 y i + 10 i

Rewrite

8 + 2 y i + 10 i

in standard complex form:

8 + (2 y + 10) i

4 x - 4 y i = 8 + (2 y + 10) i

Complex numbers can be equal only if their real and imaginary parts are equalRewrite as system of equations:

[4 x = 8 - 4 y = 2 y + 10]

[4 x = 8 - 4 y = 2 y + 10] : x = 2, y = - \frac{5}{3}

x = 2, y = - \frac{5}{3}

(1 + 2 i) x + (3 - 5 i) y = 1 - 3 i

r (t) = t^{3} i + t^{2} j

z^{2} = - 2 + 23 i

x^{2} = 1 + i

∣ 2 z - i ∣ = 4

What is the answer to 4(x-yi)=8+2yi+10i ?
The answer to 4(x-yi)=8+2yi+10i is x=2,y=-5/3