What is the value of a and b given that the product of a + 3i and 6 + bi is 4

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The product of a + 3i and 6 + bi is 4.

(a + 3i)(6 +bi) = 4

=> 6a + 18i + abi + 3bi^2 = 4

=> 6a + 18i + abi - 3b = 4

6a - 3b = 4 and 18 + ab = 0

6a - 3b = 4 => a = (4 +3b)/6

18 + ab = 0

=> `18 + b*(4 +3b)/6 = 0`

=> `3b^2 + 4b + 108 = 0`

`b = (-4 +- sqrt(16 - 1296))/6`

= `(-2 +- i*8*sqrt 5)/3`

a = `(4 +3b)/6 = (4 + 3*(-2+-i*8*sqrt 5)/3)/6`

= `(4 -2+-i*8*sqrt 5)/6`

= `(2+i*8*sqrt 5)/6`

**The value of a and b is **`((2+-i*8*sqrt 5)/6, (-2+-i*8*sqrt 5)/3)`

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