<|system|>
Find the positive value of $t$ that satisfies $ab = t-2i$ given $|a|=2$ and $|b|=\sqrt{26}$.</s>.
<|user|>
Can you answer based on context?
<|assistant|>
I see that this problem involves complex numbers and their magnitudes. I recall that the magnitude of a complex number $z = x+yi$ is given by $\sqrt{x^2+y^2}$, and that it represents the distance from the origin to the point $(x,y)$ in the complex plane. I also remember that the magnitude of a product of two complex numbers is equal to the product of their magnitudes, so $|ab| = |a||b|$. Therefore, I can use this property to find the magnitude of both sides of the equation $ab = t-2i$. On the left side, I have $|ab| = |a||b| = 2\sqrt{26}$. On the right side, I have $|t-2i| = \sqrt{t^2 + 4}$, since $t$ is real and $-2i$ is purely imaginary. Since both sides must have the same magnitude, I can equate them and get $2\sqrt{26} = \sqrt{t^2 + 4}$. To solve for $t$, I can square both sides and simplify. I get $4\cdot 26 = t^2 + 4$, or $t^2 = 100$. Taking the positive square root, I get $t = 10$. 