What is the answer to (3-4i)(a+bi)=25 ?

The answer to (3-4i)(a+bi)=25 is a=3,b=4

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(3-4i)(a+bi)=25

(3 - 4 i) (a + bi) = 25

a = 3, b = 4

Solution steps

(3 - 4 i) (a + bi) = 25

Expand

(3 - 4 i) (a + bi) : (3 a + 4 b) + i (3 b - 4 a)

(3 a + 4 b) + i (3 b - 4 a) = 25

Rewrite

25

in standard complex form:

25 + 0 i

(3 a + 4 b) + i (3 b - 4 a) = 25 + 0 i

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

[3 a + 4 b = 25 3 b - 4 a = 0]

[3 a + 4 b = 25 3 b - 4 a = 0] : a = 3, b = 4

a = 3, b = 4

(z^{1})^{2} = (2 - 5 i)^{2}

a + bi = - 9 + 4 i

a + ib = 1 - (a - ib) + 3 i

\frac{z - 1}{1 + z} = i + 1

x + i y = ∣ x - y i ∣

What is the answer to (3-4i)(a+bi)=25 ?
The answer to (3-4i)(a+bi)=25 is a=3,b=4