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![z=-45 i-15.5
What are the real and imaginary parts of
z ?
Choose 1 answer:
(A)
{:[Re(z)=-45" and "],[Im(z)=-15.5]:}
(B)
{:[Re(z)=-15.5" and "],[Im(z)=-45]:}
(c)
{:[Re(z)=-45 i" and "],[Im(z)=-15.5]:}
(D)
{:[Re(z)=-15.5" and "],[Im(z)=-45 i]:}](https://externalquestionsimg-a4fuc2b6e0gtdqge.z01.azurefd.net/external-question-images/images/images/ka/Algebra-2/Complex%20numbers/Complex%20numbers%20introduction/Q-48.png)
What are the real and imaginary parts of ?Choose answer:(A)(B)(C)(D)
Full solution
Q. What are the real and imaginary parts of ?Choose answer:(A)(B)(C)(D)
- Identify complex number: Identify the real and imaginary parts of the complex number.The complex number is given as . In a complex number of the form , is the real part and is the imaginary part, where is the imaginary unit.
- Extract real and imaginary parts: Extract the real and imaginary parts from the given complex number.For , the real part is and the imaginary part is . However, we usually write the imaginary part without the imaginary unit when specifying it as a part of the complex number.
- Write down parts separately: Write down the real and imaginary parts separately.Re() = and Im() = (without the ).
- Match parts with choices: Match the real and imaginary parts with the given choices.The correct choice that matches our findings is:(A) \{:[\text{Re}(z)=-45\text{＂ and ＂}],[\text{Im}(z)=-15.5]:}This is incorrect because it swaps the real and imaginary parts.(B) \{:[\text{Re}(z)=-15.5\text{＂ and ＂}],[\text{Im}(z)=-45]:}This is incorrect because it does not include the imaginary unit with the imaginary part.(C) \{:[\text{Re}(z)=-45 i\text{＂ and ＂}],[\text{Im}(z)=-15.5]:}This is incorrect because it includes the imaginary unit with the real part.(D) \{:[\text{Re}(z)=-15.5\text{＂ and ＂}],[\text{Im}(z)=-45 i]:}This is the correct choice because it correctly identifies the real part as and the imaginary part as .
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