How do you find the absolute value of 1+3i?

Answered question

2022-01-17

How do you find the absolute value of 1+3i?

Answer & Explanation

nick1337

nick1337

Expert2022-01-18Added 699 answers

Step 1 |1+3i|=10 The absolute value of a complex number is its distance from the origin 0 in the complex plane. By Pythagoras
Vasquez

Vasquez

Expert2022-01-18Added 597 answers

Step 1 For a complex number a+bi, polar form is given by r(cos(θ)+isin(θ)), where r=a2+b2 and θ=atan(ba) We have that a=1 and b=3 Thus, r=(1)2+(3)2=10 Also, θ=atan(31)=atan(3) Therefore, 1+3i=10(cos(atan(3))+isin(atan(3)))
alenahelenash

alenahelenash

Skilled2022-01-24Added 488 answers

Step 1 The inverse of 1+3i is 11+3i In general case, multiply the expression 1a+ib by the conjugate (the conjugate of a+ib is aib): 1a+ib=1(aib)(a+ib)(aib) Expand the denominator: 1(aib)(a+ib)(aib)=aiba2+b2 Split: aiba2+b2=aa2+b2iba2+b2 In our case, a=1 and b=3 Therefore, (11+3i)=(1103i|10) Hence, 11+3i=1103i10

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