1)What is the product of 5+ Radical (-36) and 1-Radical (-49) expressed in simplest a+bi Form?
2) Express Radical (-27) + i^22 + 3-Radical (-25) +5 Radical (-3) in simplest a+bi form.
(5 + √-36)(1-√-49)
= (5 + 6i)(1 - 7i)
= 5 - 35i + 6i - 42i^2
= 5 - 29i + 42
= 49 - 29i
2) √-27 + i^22 + 3 - √-25 + 5√-3
= 3√3i + (-1) + 3 - 5i + 5√3i
= 8√3i - 5i + 2
= (8√3 - 5)i + 2
Try '42'. It is the answer to Life, the Universe, and Everything.
12,8 and 3,-4
pnus
To get the product of expressions involving radicals and express it in simplest a+bi form, follow these steps:
1) Simplify the radicals.
For example, in the first expression, √(-36) can be simplified as √(-1 * 6^2), which becomes 6i. Similarly, √(-49) can be simplified as √(-1 * 7^2), which becomes 7i.
2) Evaluate the arithmetic operations.
In the first expression, 5 + 6i and 1 - 7i already have simplified radicals, so you can directly multiply them:
(5 + 6i) * (1 - 7i) = 5 - 35i + 6i - 42i^2
Remember that i^2 is equal to -1, so you can substitute it:
= 5 - 35i + 6i + 42
= 47 - 29i
Therefore, the product of 5 + √(-36) and 1 - √(-49) expressed in simplest a+bi form is 47 - 29i.
Similarly, for the second expression:
1) Simplify the radicals.
√(-27) can be simplified as √(-1 * 3^3), which becomes 3i√3.
√(-25) can be simplified as √(-1 * 5^2), which becomes 5i.
√(-3) can be simplified as √(-1 * 1^3), which becomes i√3.
2) Evaluate the arithmetic operations.
Simply add up all the terms:
√(-27) + i^22 + 3 - √(-25) + 5√(-3)
= 3i√3 + (-1) + 3 + 5i - i√3
Combining like terms:
= 3 + (-1) + 3 + 5i + 3i√3 - i√3
= 5 + 5i
Therefore, the expression √(-27) + i^22 + 3 - √(-25) + 5√(-3) expressed in simplest a+bi form is 5 + 5i.