Dividing Complex Numbers
Read this topicExplanations 3
- When we have an fraction with iii in both the numerator and the denominator, we want to transform the fraction back to standard form: xi+yxi + yxi+y, where xxx and yyy are real …
By Vivian Loh, Alex Federspiel
- (Video) Dividing Complex Numbers by mathman1024 In this video by mathman1024 he shows you how to divide complex numbers. The trick to solve these is to multiply both top and bot…
By Alex Federspiel, Jonathan Heller, Anusha Rahman
- Now that we've covered multiplying complex numbers, let's move on to dividing! Dividing Complex Numbers When dividing two complex numbers, there is a general pattern that you ca…
By Anusha Rahman
Problems 26
- Write 3+4i2−6i\frac{3+4i}{2-6i}2−6i3+4i as complex number in rectangular form.
- Compute the value of 12+5i2+i\dfrac{12+5i}{2+i}2+i12+5i in the form a±bi.a\pm bi.a±bi.
- Compute the quotient 4+3i2−i\frac{4+3i}{2-i}2−i4+3i, written in the form a+bia+bia+bi.
- There are integers a,ba,ba,b such that 2⋅3=(1+−5)(a+b−5)2\cdot 3 = (1+\sqrt{-5})(a+b\sqrt{-5})2⋅3=(1+−5)(a+b−5). What is a+b?a+b?a+b?
- What is the value of the quotient 2+3i1+6i\frac{2+3i}{1+6i}1+6i2+3i?
- Find the value of kkk, given that the quotient 2−kik−i\frac{2-ki}{k-i}k−i2−ki is a purely imaginary number.
- Simplify: 5i\frac{5}{i}i5
- Simplify: 4i7+i\frac{4i}{7+i}7+i4i
- Simplify: 2−3i\frac{2}{-3i}−3i2
- Simplify: −2−2i3−2i\frac{-2-2i}{3-2i}3−2i−2−2i
- Simplify: i4i5\frac{i^4}{i^5}i5i4
- Simplify: 10i−5−i\frac{10i}{-5-i}−5−i10i
- Simplify: 3i6+4i\frac{3i}{6+4i}6+4i3i
- Simplify: 5+2i1−4i\frac{5+2i}{1-4i}1−4i5+2i
- Simplify: (9+3i)23−i\frac{(9+3i)^2}{3-i}3−i(9+3i)2
- Simplify: 8i3\frac{8}{i^3}i38
- Simplify: i−1i\frac{i-1}{i}ii−1
- Simplify: 5+i5+2i\frac{5+i}{5+2i}5+2i5+i
- Simplify: 5+2i5+i\frac{5+2i}{5+i}5+i5+2i
- Simplify: a−ba+bi\frac{a-b}{a+bi}a+bia−b
- Simplify: aba−bi\frac{ab}{a-bi}a−biab
- Make the denominator real for a complex number z=a+bi,b≠0z=a+bi, b\neq 0z=a+bi,b=0: zz‾\frac{z}{\overline{z}}zz
- Simplify: 9−i−7i\frac{9-i}{-7i}−7i9−i
- Divide 6+7i3−2i\dfrac{6+7i}{3-2i}3−2i6+7i.
- Divide 1−3i1+2i\dfrac{1-3i}{1+2i}1+2i1−3i
- Divide 3+5i2+6i\dfrac{3+5i}{2+6i}2+6i3+5i