Problem

Multiply. \[ (-7+2 i)(6-5 i) \] \[ (-7+2 i)(6-5 i)= \] (Simplify your answer. Type your answer in the form $a+b i$.)

Solution

Step 1 :Given the complex numbers $(-7+2 i)$ and $(6-5 i)$, we are asked to find their product.

Step 2 :We can use the distributive property of multiplication over addition, which states that for all complex numbers a, b, and c, the equation $(a + b)c = ac + bc$ holds.

Step 3 :Applying this property, we distribute the complex number $(-7 + 2i)$ over the complex number $(6 - 5i)$ to get the product.

Step 4 :Performing the multiplication, we get $(-7+2 i)(6-5 i) = -32 + 47i$.

Step 5 :Thus, the product of the complex numbers $(-7+2 i)$ and $(6-5 i)$ is \(\boxed{-32 + 47i}\).

From Solvely APP
Source: https://solvelyapp.com/problems/aWldlQLf9v/

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