Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Multiply and simplify the following complex numbers: (5+2i)*(-5-i)

Multiply and simplify the following complex numbers:\newline(5+2i)⋅(−5−i) (5+2 i) \cdot(-5-i)

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Grade 8right chevron icon
Multiply numbers written in scientific notationright chevron icon

Full solution

Q. Multiply and simplify the following complex numbers:\newline(5+2i)⋅(−5−i) (5+2 i) \cdot(-5-i)
  1. Distribute terms: Distribute each term of the first complex number by each term of the second complex number.\newline(5+2i)(−5−i)=5(−5)+5(−i)+2i(−5)+2i(−i)(5+2i)(-5-i) = 5(-5) + 5(-i) + 2i(-5) + 2i(-i)
  2. Multiply real and imaginary parts: Multiply the real parts and the imaginary parts separately.\newline5⋅(−5)=−255\cdot(-5) = -25 (Real part)\newline5⋅(−i)=−5i5\cdot(-i) = -5i (Imaginary part)\newline2i⋅(−5)=−10i2i\cdot(-5) = -10i (Imaginary part)\newline2i⋅(−i)=2i22i\cdot(-i) = 2i^2 (Since i2=−1i^2 = -1, this will result in a real number)
  3. Combine like terms: Combine the like terms and simplify the expression.−25+(−5i)+(−10i)+2(−1)=−25−5i−10i−2-25 + (-5i) + (-10i) + 2(-1) = -25 - 5i - 10i - 2
  4. Add real and imaginary numbers: Add the real numbers and the imaginary numbers separately.\newline(−25−2)+(−5i−10i)=−27−15i(-25 - 2) + (-5i - 10i) = -27 - 15i
  5. Final simplified form: Write the final simplified form of the product of the two complex numbers.\newlineThe product is −27−15i-27 - 15i.

More problems from Multiply numbers written in scientific notation

Question
Multiply and simplify the following complex numbers:\newline(4+4i)⋅(−2−5i) (4+4 i) \cdot(-2-5 i)
Get tutor helpright-arrow

Posted 3 months ago

Question
Multiply and simplify the following complex numbers:\newline(3−4i)⋅(−3+2i) (3-4 i) \cdot(-3+2 i)
Get tutor helpright-arrow

Posted 3 months ago

Question
Multiply and simplify the following complex numbers:\newline(5−5i)⋅(−3+5i) (5-5 i) \cdot(-3+5 i)
Get tutor helpright-arrow

Posted 3 months ago

Question
Find lim⁡x→4x−43−x+5 \lim _{x \rightarrow 4} \frac{x-4}{3-\sqrt{x+5}} .\newlineChoose 11 answer:\newline(A) −6-6\newline(B) −43 -\frac{4}{3} \newline(C) −103 -\frac{10}{3} \newlineD The limit doesn't exist
Get tutor helpright-arrow

Posted 3 months ago

Question
Consider the following problem:\newlineThe population of ants in Chloe's ant farm changes at a rate of r(t)=−15.8⋅0.9t r(t)=-15.8 \cdot 0.9^{t} ants per month (where t t is time in months). At time t=0 t=0 , the ant farm's population is 150150 ants. How many ants are in the farm at t=4 t=4 ?\newlineWhich expression can we use to solve the problem?\newlineChoose 11 answer:\newline(A) ∫04r(t)dt \int_{0}^{4} r(t) d t \newline(B) ∫34r(t)dt \int_{3}^{4} r(t) d t \newline(C) 150+∫34r(t)dt 150+\int_{3}^{4} r(t) d t \newline(D) 150+∫04r(t)dt 150+\int_{0}^{4} r(t) d t
Get tutor helpright-arrow

Posted 3 months ago

Question
99[44−7-7(x−1-1)]+44[(22x+55)−7-7]=1111x−332-332\newlineThe solution set is \{\} . (Type an integer or a simplifed fra
Get tutor helpright-arrow

Posted 2 months ago

Question
Write the answer in proper scientific notation:\newline(0.06×10−4)3(0.06 \times 10^{-4})^{3}
Get tutor helpright-arrow

Posted 2 months ago

Question
Write the answer in proper scientific notation:\newline(0.002×106)−4(0.002 \times 10^{6})^{-4}
Get tutor helpright-arrow

Posted 2 months ago

Question
Write the answer in proper scientific notation:\newline(5,000×10−1)−3(5,000 \times 10^{-1})^{-3}
Get tutor helpright-arrow

Posted 2 months ago

Question
The price of a visit to the dentist is $50\$50. If the dentist fills any cavities, an additional charge of $100\$100 per cavity gets added to the bill. If the dentist finds nn cavities, what will the cost of the visit be? Write your answer as an expression.
Get tutor helpright-arrow

Posted 11 hours ago

View all (4)