What is the answer to (4+xi)/(2+i)=y+2i ?

The answer to (4+xi)/(2+i)=y+2i is x=7,y=3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(4+xi)/(2+i)=y+2i

\frac{4 + x i}{2 + i} = y + 2 i

x = 7, y = 3

Solution steps

\frac{4 + x i}{2 + i} = y + 2 i

Multiply both sides by

2 + i

\frac{4 + x i}{2 + i} (2 + i) = y (2 + i) + 2 i (2 + i)

Expand

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

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

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

[4 = 2 y - 2 x = 4 + y] : x = 7, y = 3

x = 7, y = 3

(a - 1) + (b + 3) i = 5 + 8 i

(x - i y)^{2} = 4 (x + i y)

z^{2} + (2 i - 3) z + 5 - i = 0

z^{2} - (5 - 4 i) z + (3 - 11 i) = 0

z^{2} + 2 \cdot i \cdot z - 1 - i = 0

What is the answer to (4+xi)/(2+i)=y+2i ?
The answer to (4+xi)/(2+i)=y+2i is x=7,y=3