(-5%2B7i).jpeg "(-3+5i)(-5+7i)")
Multiplying Complex Numbers: (-3 + 5i)(-5 + 7i)
This article will guide you through multiplying two complex numbers: (-3 + 5i) and (-5 + 7i).
Understanding Complex Numbers
Complex numbers are numbers that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit, defined as the square root of -1.
Multiplication Process
Multiplying complex numbers is similar to multiplying binomials. We use the distributive property (or FOIL method) to expand the product:
(-3 + 5i)(-5 + 7i) = (-3)(-5) + (-3)(7i) + (5i)(-5) + (5i)(7i)
Simplifying the terms:
= 15 - 21i - 25i + 35i²
Dealing with i²
Recall that i² = -1. Substituting this value into our equation:
= 15 - 21i - 25i + 35(-1)
Combining Real and Imaginary Terms
Now, we group the real terms and the imaginary terms:
= (15 - 35) + (-21 - 25)i
Final Result
Simplifying the equation, we get the final result:
= -20 - 46i
Therefore, the product of (-3 + 5i) and (-5 + 7i) is -20 - 46i.