73.8k views
1 vote
Divide 3+I By 2-3i.. Write Down Your Work

1 Answer

4 votes

Sure, let's divide two complex numbers step by step.

We are given the complex numbers (3+1i) and (2-3i). Our goal is to divide these two complex numbers.

To find the quotient of two complex numbers, we multiply the numerator and the denominator by the conjugate of the denominator.

The conjugate of a complex number (a+bi) is the complex number (a-bi). So, the conjugate of (2-3i) is (2+3i).

Consider the division (3+1i) / (2-3i)

We start by multiplying both the numerator and the denominator by the conjugate of the denominator, which is (2+3i).

= ((3+1i)(2+3i)) / ((2-3i)(2+3i))
= (6+9i+2i+3) / ((4+6i-6i-9))
= (9+11i) / (4-9)
= (9+11i) / -5

We split the fraction into real and imaginary parts:

= 9/-5 + 11i/-5
= -9/5 - 11i/5

So, the result of the division (3+1i) / (2-3i) is -9/5 - 11i/5.

User Sasigarn
by
8.4k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories