Question

real part and imaginary part of the complex number z= -3+i√7

Answer 1

Given

⇒Z = -3 + i√7

To find

⇒Real Part and Imaginary Part

Now we get

⇒Re( Z ) or Real Part of Z = -3

⇒Im(Z) or Imaginary part of Z = √7

More Information about Complex Number

⇒i = √(-1)

⇒i² = -1

⇒i³ = -i

⇒i⁴ = 1

⇒1/i = -i

⇒i + i² + i³ + i⁴ = 0

⇒If im(Z) = 0 , then Z is said to be purely real

⇒If Re(Z) = 0 and Im(Z) = 0 , Z = 0 + 0i , then z is said to purely real as well as purely Imaginary

Let

⇒Z₁ = a₁ + b₁i

⇒Z₂ = a₂ + b₂i

⇒Z₁  ± Z₂

Addition And subtraction

⇒( a₁ ± a₂ ) + ( b₁ ± b₂)i

Multiplication

⇒(a₁a₂ - b₁b₂) + ( a₁b₂ + a₂b₁)i

Division

⇒(a₁a₂ + b₁b₂ )/(a₂² + b₂² ) + (a₂b₁ - a₁b₂ )/(a₂² + b₂²) × i