What is the answer to 3a-2bi=5+3i ?

The answer to 3a-2bi=5+3i is a= 5/3 ,b=-3/2

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3a-2bi=5+3i

3 a - 2 bi = 5 + 3 i

a = \frac{5}{3}, b = - \frac{3}{2}

Solution steps

3 a - 2 bi = 5 + 3 i

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

[3 a = 5 - 2 b = 3]

[3 a = 5 - 2 b = 3] : a = \frac{5}{3}, b = - \frac{3}{2}

a = \frac{5}{3}, b = - \frac{3}{2}

22 + i 22 = x^{2}

4 z^{2} - 4 (1 - 2 i) z + 1 - 4 i = 0

(3 - i) (a + bi) = - 6 - 8 i

(a + i) (2 - bi) = 7 - i

(x + y i) + (2 (x + y i) + 3 i) = 9