Home > Precalculus > Multiplication of Complex Numbers

How do you simplify #(2+3i) (1-2i) #?

Answer 1

Benjamin Achtenberg

2 -2i + 3i - 6i^2
= 2 + i + 6
= 7 + i

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Caleb Alexander

To simplify the expression ((2+3i)(1-2i)), we use the distributive property of multiplication over addition:

[ (2+3i)(1-2i) = 2 \cdot 1 + 2 \cdot (-2i) + 3i \cdot 1 + 3i \cdot (-2i) ]

Simplify each term:

[ 2 \cdot 1 = 2 ] [ 2 \cdot (-2i) = -4i ] [ 3i \cdot 1 = 3i ] [ 3i \cdot (-2i) = -6i^2 ]

Remember that (i^2 = -1), so substituting:

[ -6i^2 = -6(-1) = 6 ]

Putting it all together:

[ (2+3i)(1-2i) = 2 - 4i + 3i + 6 ]

Combine like terms:

[ 2 - 4i + 3i + 6 = 2 + (-4i + 3i) + 6 = 2 - i + 6 ]

Finally, combine the constants:

[ 2 - i + 6 = 8 - i ]

So, ((2+3i)(1-2i)) simplifies to (8 - i).

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.