Mar 23, 2017 · |2 +5i | = sqrt(29) The modulus of a complex number a+bi is given by: |a +bi | = sqrt(a^2+b^2) Thus; |2 +5i | = sqrt(2^2+5^2) " " = sqrt(4+25) " " = sqrt(29)

Jan 27, 2016 · -21+20i First, distribute this using FOIL as you normally would a binomial. (2+5i)^2=(2+5i)(2+5i)= overbrace(2xx2)^("First")+overbrace(2xx5i)^"Outside"+overbrace(5ixx2)^"Inside"+overbrace(5ixx5i)^"Last" This gives 4+10i+10i+25i^2 or 4+20i+25i^2 While this may look simplified, we can go one step further. Since i=sqrt(-1), we know that i^2=-1, so we can replace i^2 with -1, giving: 4+20i+25( …

Jan 11, 2016 · (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.

Jan 8, 2017 · The difference of squares identity can be written: #a^2-b^2 = (a-b)(a+b)# So we find: #(5-2i)(5+2i) = 5^2-(2i)^2 = 25+4 = 29#

Jan 13, 2016 · 20/ 29 + 21/29 i To divide (2+5i)/(5+2i), you need to find the complex conjugate of the denominator and extend the fraction with it. This way, you will be able to "get rid" of the i in the denominator. Let me walk you through the process: Your denominator is 5 + 2i, thus the complex conjugate is 5 - 2i.

Nov 12, 2016 · (2-4i)(3+5i) =26-2i (2-4i)(3+5i) =(2)(3)+(2)(5i)+(-4i)(3)+(-4i)(5i) :. (2-4i)(3+5i) =6+10i-12i-20i^2 :. (2-4i)(3+5i) =6-2i-20i^2 Now i^2=-1, so :. (2-4i)(3+5i) =6-2i ...

Dec 26, 2016 · 2i-5 You can multiply the terms of the fraction by i and get: ((2+5i)i)/(-i*i)=(2i+5i^2)/(-i^2) and, since i^2=-1: (2i-5)/1=2i-5

Aug 31, 2016 · (2-5i)(p+q)i=29i While multiplying complex numbers we should remember that i^2=-1. As p=2 and q=5i, (2-5i ...

Jan 31, 2016 · To simplify a complex fraction, multiply top and bottom (denominator and numerator) by the complex conjugate of the bottom. This expression simplifies to (2-5i)/29. The 'complex conjugate' of a complex number (a+bi) is (a-bi), and multiplying a complex number by its complex conjugate will yield a real number. 1/(2+5i)*(2-5i)/(2-5i) Note that (2-5i)/(2-5i) = 1 so we are not changing the ...

Aug 28, 2016 · (4+5i)/(2-5i)=-17/29+30/29i We should always remember two things while dividing a complex number by another. One - multiply numerator and denominator each by complex conjugate of the Divi