How do you write 3 -3i in exponential form?

1 Answer
1s2s2p
Apr 26, 2018

#3sqrt2e^(i(7pi)/4)#

Explanation:

#z=a+bi=re^(itheta)#, where:

  • #r=sqrt(a^2+b^2)#
  • #theta=tan^-1(b/a)#

#r=sqrt(3^2+3^2)=sqrt18=3sqrt2#

#theta=tan^-1(-1)=-pi/4#, however since #3-3i# is in quadrant 4 we have to add #2pi# to find the positive angle for the same point (since adding #2pi# is going around in a circle).

#2pi-pi/4=(7pi)/4#

#3sqrt2e^(i(7pi)/4)#

Related questions
Impact of this question
2532 views around the world
You can reuse this answer
Creative Commons License