What is the answer to a/(1+i)+b/(1+2i)=1 ?

The answer to a/(1+i)+b/(1+2i)=1 is a=4,b=-5

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a/(1+i)+b/(1+2i)=1

\frac{a}{1 + i} + \frac{b}{1 + 2 i} = 1

a = 4, b = - 5

Solution steps

\frac{a}{1 + i} + \frac{b}{1 + 2 i} = 1

Find Least Common Multiplier of

1 + i, 1 + 2 i : (1 + i) (1 + 2 i)

Multiply by LCM=

(1 + i) (1 + 2 i)

\frac{a}{1 + i} (1 + i) (1 + 2 i) + \frac{b}{1 + 2 i} (1 + i) (1 + 2 i) = 1 \cdot (1 + i) (1 + 2 i)

Simplify

(a + b) + i (b + 2 a) = - 1 + 3 i

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

[a + b = - 1 b + 2 a = 3]

[a + b = - 1 b + 2 a = 3] : a = 4, b = - 5

a = 4, b = - 5

(3 + 2 i) x^{2} + 10 x + 2 = 0

a = bi

i x^{2} - 3 x - 2 i = 0

z^{2} + 2 i z - 5 = 0

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

What is the answer to a/(1+i)+b/(1+2i)=1 ?
The answer to a/(1+i)+b/(1+2i)=1 is a=4,b=-5