Question 5 of 28beginner🔧 ApplyNumerical1 mark

Express the following complex number in the form a+iba + ib: (1−i)−(−1+i6)(1 - i) - (-1 + i6)

Correct Answer

2 - 7i

Exercise: EXERCISE 4.1 | Q: 5 | (Page 7)
For More Understanding

Explanation

This question tests the subtraction of complex numbers. According to the context, for complex numbers z₁ = a + ib and z₂ = c + id, subtraction follows the pattern of combining real parts and imaginary parts separately. The student needs to distribute the negative sign properly and then group real and imaginary terms.

Solution Steps

  1. Step 1: Write the given expression: (1−i)−(−1+i6)(1 - i) - (-1 + i6)

  2. Step 2: Distribute the negative sign to the second complex number: =1−i+1−i6= 1 - i + 1 - i6

  3. Step 3: Group the real parts and imaginary parts: =(1+1)+(−1−6)i= (1 + 1) + (-1 - 6)i

  4. Step 4: Simplify: =2−7i= 2 - 7i

  5. Final Answer: The complex number in the form a+iba + ib is 2−7i2 - 7i, where a=2a = 2 and b=−7b = -7.

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