Math Problem Statement
13i/10i(5-3i)
Solution
Let's simplify the expression:
Step 1: Simplify the denominator
Multiply the denominator:
Recall that , so:
Thus, the expression becomes:
Step 2: Rationalize the denominator
To remove the imaginary part from the denominator, multiply both the numerator and the denominator by the conjugate of the denominator, :
Step 3: Multiply the numerator and simplify
First, let's expand the numerator:
Since :
Step 4: Multiply the denominator
Now expand the denominator:
Since :
Step 5: Final answer
Now, the expression becomes:
We can simplify this by dividing both the real and imaginary parts by 3400:
Thus, the simplified form of the expression is:
Do you want more details or have any questions?
Here are 5 related questions to practice:
- Simplify .
- Rationalize and simplify .
- Find the conjugate of .
- Simplify .
- Multiply and simplify.
Tip: Always remember that when simplifying complex numbers.
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Math Problem Analysis
Mathematical Concepts
Complex Numbers
Rationalization
Multiplication of Complex Numbers
Formulas
i^2 = -1
Rationalizing complex numbers by multiplying by the conjugate: (a + bi)(a - bi) = a^2 - b^2i^2
Theorems
Rationalization of Complex Numbers
Suitable Grade Level
Grades 10-12