What is the answer to x+3i=(1+yi)(2-3i) ?

The answer to x+3i=(1+yi)(2-3i) is x=11,y=3

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x+3i=(1+yi)(2-3i)

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

x = 11, y = 3

Solution steps

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

Expand

(1 + y i) (2 - 3 i) : (2 + 3 y) + i (- 3 + 2 y)

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

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

[x = 2 + 3 y 3 = - 3 + 2 y]

[x = 2 + 3 y 3 = - 3 + 2 y] : x = 11, y = 3

x = 11, y = 3

x^{2} + (1 - 2 i) x - 2 i = 0

z^{2} - 3 + 2 i = 0, z

zz = 13 - 13 i

x^{2} + 1 = i

a^{2} + b^{2} + a - bi = 11 + 3 i

What is the answer to x+3i=(1+yi)(2-3i) ?
The answer to x+3i=(1+yi)(2-3i) is x=11,y=3