Perform the operation and write the result in standard form.
8 + 20i over 2i
Please explain, I am very confused!!
i is a symbol such that
i2 = -1
To calculate (8+20i)/i
multiply top and bottom by i, and substitute all i2 by -1.
(8+20i)/i
=(8+20i)i/i*i
=(8i+20i2)/(i2)
=(8i-20)/(-1)
=20-8i
To perform the given operation and write the result in standard form, we need to simplify the expression by rationalizing the denominator.
Step 1: Begin by multiplying both the numerator and the denominator by the conjugate of the denominator. In this case, the conjugate of 2i is -2i.
(8 + 20i) / 2i * (-2i) / (-2i)
Step 2: Simplify the expression by using the properties of complex numbers. When multiplying complex conjugates, the result is always a real number.
((-2i)(8 + 20i)) / (-2i)(2i)
Step 3: Multiply the complex terms and distribute to simplify the expression.
(-16i - 40i^2) / (-2i^2)
Step 4: Simplify further by substituting the values of i^2 (-1).
(-16i - 40(-1)) / (-2(-1))
Step 5: Continue to simplify the expression.
(-16i + 40) / 2
Step 6: Divide both the numerator and the denominator by 2.
-8i + 20 / 1
Step 7: Write the result in standard form by separating the real and imaginary parts.
20 - 8i
Therefore, the result of the given operation in standard form is 20 - 8i.