Algebra 2 - How to divide complex numbers (-5-9i) / (9+8i)

The video tutorial explains how to divide complex numbers using conjugates. It begins by discussing the initial approach of multiplying by i over i and highlights the limitations when dealing with binomials. The teacher introduces the concept of conjugates and demonstrates how to multiply binomials in both the numerator and denominator. The tutorial concludes with simplifying the expression by combining like terms and using the property of i squared.

What is the initial step when dividing complex numbers with a binomial denominator?

• Add the real parts

• Multiply by i over i

• Subtract the imaginary parts

• Use the conjugate of the denominator

Why can't we simply multiply by 'i' when the denominator is a binomial?

• It eliminates the real part

• It makes the expression more complex

• It only works for monomials

• It doesn't change the denominator

What is the conjugate of a complex number?

• The negative of the number

• The reciprocal of the number

• The same number with the opposite sign of the real part

• The same number with the opposite sign of the imaginary part

What is the result of multiplying two conjugates?

• A complex number

• An imaginary number

• A real number

• Zero

What happens to the imaginary terms when multiplying the conjugates?

• They cancel out

• They double

• They become real

• They remain unchanged

How do you simplify the expression after multiplying the conjugates?

• Divide by the real part

• Combine like terms

• Subtract the real parts

• Add the imaginary parts

What is the final form of the expression after simplification?

• Two separate fractions

• An imaginary number

• A single complex number

• A real number