Find the sum and the product of the complex numbers 3−2i and −3+5i.

Question

temzej9 · Accepted Answer

Step 1  Consider the complex numbers 3−2i and −3+5i.  To find the sum of the complex numbers, add/subtract the real part with real and the imaginary part with the imaginary part.  So the sum of the complex numbers is  (3−2i)+(−3+5i)=3−2i−3+5i  =3−3−2i+5i  =0+3i  =3i  Thus, the sum of the complex numbers is 3i.  Step 2  To find the product of the complex number, use FOIL method to multiply the binomials and simplify further as shown below  (3−2i)(−3+5i)=3×(−3)+3×(5i)−2i×(−3)−2i×(5i)  =−9+15i+6i−10i2  =−9+21i−10(−1)(i2=−1)  =−9+21i+10  =1+21i  Thus, the product of the complex numbers is 1+21i

limacarp4 · Accepted Answer

Step 1  Complex number:  1) 3−2i  2) −3+5i  Add: (1)+(2)=(3−2i)+(−3+5i)=(3−3)+(−2+5)i=3i  Step 2  (3−2i)(−3+5i)  Apply complex arithmetric rule:  (a+bi)(c+di)=(ac−bd)+(ad+bc)i  a=3, b=−2, c=−3, d=5  =(3(−3)−(−2)×5)+(3×5+(−2)(−3))i  3(−3)−(−2)×5=1  3×5+(−2)(−3)=21  =1+21i

Vasquez · Accepted Answer

Step 1 (3−2i)+(−3+5t) Group the real part and the imaginary part of the complex number (a+bi)±(c+dt)=(a±c)+(b±d)i=(3−3)+(−2+5)i3−3=0−2+5=3=0+3i=0+3iStep 2Multiple: (3−2i)×(−3+5i)=3×(−3)+3×5i+(−2i)×(−3)+(−2i)×5i=−9+15i+6i−10i2=−9+15i+6i+10=−9+10+i(15+6)=1+21i

Find the sum and the product of the complex numbers

Answered question

Answer & Explanation

New Questions in Precalculus