Home > Precalculus > Division of Complex Numbers

How do you simplify #(2+5i)/ (1-i)#?

Answer 1

#(2+5i)/(1-i)= -3/2 + 7/2i#

The conjugate of a complex number #a+bi# is #a-bi#. The product of a complex number and its conjugate is a real number. We will use this fact to produce a real number in the denominator by multiplying the numerator and denominator by the conjugate of the denominator.

#(2+5i)/(1-i) = (2+5i)/(1-i)*(1+i)/(1+i)#

#= (2 + 5i + 2i - 5)/(1 + i - i + 1)#

# = (-3+7i)/2#

#= -3/2 + 7/2i#

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.

Trending questions

Not the question you need?

HIX Tutor

Solve ANY homework problem with a smart AI

98% accuracy study help
Covers math, physics, chemistry, biology, and more
Step-by-step, in-depth guides
Readily available 24/7