What is the answer to (1+2i)a+(3-5i)b=1-3i ?

The answer to (1+2i)a+(3-5i)b=1-3i is a=-4/11 ,b= 5/11

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(1+2i)a+(3-5i)b=1-3i

(1 + 2 i) a + (3 - 5 i) b = 1 - 3 i

a = - \frac{4}{11}, b = \frac{5}{11}

Solution steps

(1 + 2 i) a + (3 - 5 i) b = 1 - 3 i

Rewrite

(1 + 2 i) a + (3 - 5 i) b

in standard complex form:

(a + 3 b) + (2 a - 5 b) i

(a + 3 b) + (2 a - 5 b) i = 1 - 3 i

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

[a + 3 b = 1 2 a - 5 b = - 3]

[a + 3 b = 1 2 a - 5 b = - 3] : a = - \frac{4}{11}, b = \frac{5}{11}

a = - \frac{4}{11}, b = \frac{5}{11}

7 x + x i - 3 y i = 3 y + 9

(x + y i) (2 - 4 i) = 14 - 18 i

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

∣ z + 3 ∣ = 1 - i z

2 x + 8 i = 6 - (2 y) i

What is the answer to (1+2i)a+(3-5i)b=1-3i ?
The answer to (1+2i)a+(3-5i)b=1-3i is a=-4/11 ,b= 5/11