Question 1 of 28beginner🔧 ApplyNumerical1 mark

Express the following complex number in the form a+iba + ib: (5i)(−35i)(5i)\left(-\frac{3}{5}i\right)

Correct Answer

3

Exercise: EXERCISE 4.1 | Q: 1 | (Page 7)
For More Understanding

Explanation

This is Exercise 4.1, Question 1 from the NCERT textbook. The problem requires multiplying two purely imaginary numbers and expressing the result in standard form a + ib. Using the fundamental property that i² = -1 (established in section 4.2 of the context), the multiplication simplifies to a real number.

Solution Steps

  1. Step 1: Multiply the coefficients and the imaginary units: (5i)(−35i)=5×(−35)×i×i=−3i2(5i)\left(-\frac{3}{5}i\right) = 5 \times \left(-\frac{3}{5}\right) \times i \times i = -3i^2

  2. Step 2: Apply the property i2=−1i^2 = -1 (from the context: "we have i2=−1i^2 = -1"): −3i2=−3(−1)=3-3i^2 = -3(-1) = 3

  3. Step 3: Express in the form a+iba + ib: 3=3+0i3 = 3 + 0i, where a=3a = 3 and b=0b = 0

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