If z = -1 + i, what is the square of the modulus of z?
Practice Questions
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If z = -1 + i, what is the square of the modulus of z?
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Questions & Step-by-Step Solutions
If z = -1 + i, what is the square of the modulus of z?
Step 1: Identify the complex number z, which is given as z = -1 + i.
Step 2: Recall that the modulus of a complex number z = a + bi is calculated using the formula |z| = √(a² + b²), where a is the real part and b is the imaginary part.
Step 3: In our case, the real part a is -1 and the imaginary part b is 1.
Step 4: Substitute the values of a and b into the modulus formula: |z| = √((-1)² + 1²).
Step 5: Calculate (-1)², which is 1, and 1², which is also 1.
Step 6: Add the results: 1 + 1 = 2.
Step 7: Take the square root of 2: |z| = √2.
Step 8: To find the square of the modulus, calculate |z|² = (√2)².
