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Express the following in standard form : (2 –; √3i) (2 + √3i) + 2 – 4i
a)3 + 4i
b)4i
c)6−7i
d)13 + 4i
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Express the following in standard form : (2 –; √3i) (2 + √3i) + 2 – 4i...
It is in the form of (a+b)(a-b) hence 2 square +root 3i square. (i square =-1) (4-3 (-1))+2-4i =9-4i hence proved hope that helps you.
Community Answer
Express the following in standard form : (2 –; √3i) (2 + √3i) + 2 – 4i...
To express the expression (2 – √3i) (2 + √3i) in standard form, we need to simplify the expression.
Let's start by using the formula for multiplying two complex numbers: (a + bi)(c + di) = (ac - bd) + (ad + bc)i.
Here, a = 2, b = -√3, c = 2, and d = √3.
So, we can apply the formula to simplify the expression:
(2 – √3i) (2 + √3i) = (2 * 2 - (-√3 * √3)) + (2 * √3 + 2 * -√3)i
= (4 + 3) + (2√3 - 2√3)i
= 7 + 0i
= 7
Therefore, the expression (2 – √3i) (2 + √3i) simplifies to 7.
Now, let's express the expression (2 - 4i)(3 + 4i) in standard form.
Using the same formula for multiplying complex numbers, we have:
(2 - 4i)(3 + 4i) = (2 * 3 - (-4 * 4)) + (2 * 4 + 3 * 4)i
= (6 + 16) + (8 + 12)i
= 22 + 20i
Therefore, the expression (2 - 4i)(3 + 4i) simplifies to 22 + 20i.
In standard form, a complex number is expressed as a + bi, where a and b are real numbers.
So, the expression (2 - √3i)(2 + √3i) is already in standard form, and it simplifies to 7.
The expression (2 - 4i)(3 + 4i) is not in standard form, but it simplifies to 22 + 20i, which is in standard form.
Let's start by using the formula for multiplying two complex numbers: (a + bi)(c + di) = (ac - bd) + (ad + bc)i.
Here, a = 2, b = -√3, c = 2, and d = √3.
So, we can apply the formula to simplify the expression:
(2 – √3i) (2 + √3i) = (2 * 2 - (-√3 * √3)) + (2 * √3 + 2 * -√3)i
= (4 + 3) + (2√3 - 2√3)i
= 7 + 0i
= 7
Therefore, the expression (2 – √3i) (2 + √3i) simplifies to 7.
Now, let's express the expression (2 - 4i)(3 + 4i) in standard form.
Using the same formula for multiplying complex numbers, we have:
(2 - 4i)(3 + 4i) = (2 * 3 - (-4 * 4)) + (2 * 4 + 3 * 4)i
= (6 + 16) + (8 + 12)i
= 22 + 20i
Therefore, the expression (2 - 4i)(3 + 4i) simplifies to 22 + 20i.
In standard form, a complex number is expressed as a + bi, where a and b are real numbers.
So, the expression (2 - √3i)(2 + √3i) is already in standard form, and it simplifies to 7.
The expression (2 - 4i)(3 + 4i) is not in standard form, but it simplifies to 22 + 20i, which is in standard form.
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Express the following in standard form : (2 –; √3i) (2 + √3i) + 2 – 4ia)3 + 4ib)4ic)6−7id)13 + 4iCorrect answer is option 'C'. Can you explain this answer?
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Express the following in standard form : (2 –; √3i) (2 + √3i) + 2 – 4ia)3 + 4ib)4ic)6−7id)13 + 4iCorrect answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Express the following in standard form : (2 –; √3i) (2 + √3i) + 2 – 4ia)3 + 4ib)4ic)6−7id)13 + 4iCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Express the following in standard form : (2 –; √3i) (2 + √3i) + 2 – 4ia)3 + 4ib)4ic)6−7id)13 + 4iCorrect answer is option 'C'. Can you explain this answer?.
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